%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@Comment{ The Arithmetic of Dynamical Systems }
@Comment{ Joseph H. Silverman }
@Comment{ Biblographic Database File - ArithDyn.bib }

%%%%%% Some more references from Tom

@comment{ ----- Blank form for ArXiv papers ---}
@comment{UPDATE}
@misc {arxiv,
    AUTHOR = {Z},
    TITLE = {},
     YEAR = {},
     NOTE = {\url{}},
}

@comment{
Articles preceded by
comment{UPDATE}
are preprints or "to appears" that should be updated as appropriate.
}

@comment{
%%% To fix excessive space between bibliography entries, 
%%% after creating the .bbl file using bibtex, put the following
%%% three commands after the \begin{bibliography} command. (May need
%%% to adjust the size of \itemsep to look okay.)
\setlength{\itemsep}{-4pt}
\small
\addcontentsline{toc}{chapter}{Bibliography} % not needed for amsbook.sty
}

@comment{ ------------------------------------------------------------ }
@comment{ Material to Add:}

@misc {tmp,
    AUTHOR = {Z. Zzzzzzz},
    TITLE = {Reference filler},
     YEAR = {9999},
}
@comment{ ------------------------------------------------------------ }

@preamble{
   "\def\cprime{$'$} "
}

@comment{--AAA-- }

@article {MR1732080,
    AUTHOR = {Abarenkova, N. and Angl{\`e}s d'Auriac, J.-Ch. and Boukraa, S.
              and Hassani, S. and Maillard, J.-M.},
     TITLE = {Topological entropy and {A}rnold complexity for
              two-dimensional mappings},
   JOURNAL = {Phys. Lett. A},
  FJOURNAL = {Physics Letters. A},
    VOLUME = {262},
      YEAR = {1999},
    NUMBER = {1},
     PAGES = {44--49},
      ISSN = {0375-9601},
     CODEN = {PYLAAG},
   MRCLASS = {37E30 (37B40 37C30 37C35)},
  MRNUMBER = {1732080 (2001b:37062)},
MRREVIEWER = {Joan Carles Tatjer},
       DOI = {10.1016/S0375-9601(99)00662-3},
       URL = {http://dx.doi.org/10.1016/S0375-9601(99)00662-3},
}
@comment{UPDATE}
@misc {arxiv1308.3133,
    AUTHOR = {Abram, William and  Lagarias, Jeffrey C. },
    TITLE = {Intersections of multiplicative translates of 3-adic Cantor sets},
     YEAR = {2013},
     NOTE = {\url{arXiv:1308.3133}},
}
    
@article {MR0175106,
    AUTHOR = {Adler, R. L. and Konheim, A. G. and McAndrew, M. H.},
     TITLE = {Topological entropy},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {114},
      YEAR = {1965},
     PAGES = {309--319},
      ISSN = {0002-9947},
   MRCLASS = {28.70 (54.00)},
  MRNUMBER = {0175106 (30 \#5291)},
MRREVIEWER = {J. C. Oxtoby},
}
@book {MR510197,
    AUTHOR = {Ahlfors, Lars V.},
     TITLE = {Complex {A}nalysis},
 PUBLISHER = {McGraw-Hill Book Co.},
   ADDRESS = {New York},
      YEAR = {1978},
     PAGES = {xi+331},
      ISBN = {0-07-000657-1},
   MRCLASS = {30-01},
  MRNUMBER = {MR510197 (80c:30001)},
}

@comment{UPDATE}
@misc {arxiv1909.00039,
    AUTHOR = {Ahmad, Faseeh and Benedetto, Robert L. and Cain, Jennifer and Carroll, Gregory and Fang, Lily},
    TITLE = {The arithmetic basilica: a quadratic {PCF} arboreal {G}alois group},
     YEAR = {2019},
     NOTE = {\url{arXiv:1909.00039}},
}


@comment{UPDATE}
@misc {arxiv0910.4556,
    AUTHOR = {Ahmadi, Omran},
    TITLE = {A Note on Stable Quadratic Polynomials over Fields 
          of Characteristic Two},
     YEAR = {2009},
     NOTE = {\url{arXiv:0910.4556}},
}
@comment{UPDATE}
@misc {arxiv1810.03142,
    AUTHOR = {Ahmadi, Omran and Monsef-Shokri, Kosrov},
    TITLE = {A note on the stability of trinomials over finite fields},
     YEAR = {2018},
     NOTE = {\url{arXiv:1810.03142}},
}
@article {MR2911375,
    AUTHOR = {Ahmadi, Omran and Luca, Florian and Ostafe, Alina and
              Shparlinski, Igor E.},
     TITLE = {On stable quadratic polynomials},
   JOURNAL = {Glasg. Math. J.},
  FJOURNAL = {Glasgow Mathematical Journal},
    VOLUME = {54},
      YEAR = {2012},
    NUMBER = {2},
     PAGES = {359--369},
      ISSN = {0017-0895},
   MRCLASS = {37P05 (11C08 11T06)},
  MRNUMBER = {2911375},
       DOI = {10.1017/S001708951200002X},
       URL = {http://dx.doi.org/10.1017/S001708951200002X},
}
@article {MR0335427,
    AUTHOR = {Aho, A. V. and Sloane, N. J. A.},
     TITLE = {Some doubly exponential sequences},
   JOURNAL = {Fibonacci Quart.},
  FJOURNAL = {The Fibonacci Quarterly. Official Organ of the Fibonacci
              Association},
    VOLUME = {11},
      YEAR = {1973},
    NUMBER = {4},
     PAGES = {429--437},
      ISSN = {0015-0517},
   MRCLASS = {10A40},
  MRNUMBER = {MR0335427 (49 \#209)},
MRREVIEWER = {J. B. Roberts},
}
@comment{http://www.research.att.com/~njas/doc/doubly.html, Publ. List, item 20}

@article {MR2046966,
    AUTHOR = {Ailon, Nir and Rudnick, Z{\'e}ev},
     TITLE = {Torsion points on curves and common divisors of {$a\sp k-1$}
              and {$b\sp k-1$}},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {113},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {31--38},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11D61 (11R58)},
  MRNUMBER = {MR2046966 (2004m:11045)},
MRREVIEWER = {Yann Bugeaud},
}
@article {arxiv0408170,
   AUTHOR = {Aitken, Wayne and Hajir, Farshid and Maire, Christian},
    TITLE = {Finitely ramified iterated extensions},
   JOURNAL = {IMRN},
  FJOURNAL = {International Mathematics Research Notices},
     YEAR = {2005},
    PAGES = {855--880},
   VOLUME = {14},
}
@comment{\url{ArXiv:math.NT/0408170}}

@article {MR2549537,
    AUTHOR = {Akbary, Amir and Ghioca, Dragos},
     TITLE = {Periods of orbits modulo primes},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {129},
      YEAR = {2009},
    NUMBER = {11},
     PAGES = {2831--2842},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11G35 (11G50 14G25 37Pxx)},
  MRNUMBER = {MR2549537},
       DOI = {10.1016/j.jnt.2009.03.007},
       URL = {http://dx.doi.org/10.1016/j.jnt.2009.03.007},
}

@article {arxiv0704.3674,
    AUTHOR = {Akiyama, Shigeki and Brunotte, Horst and Peth{\H{o}}, Attila
              and Steiner, Wolfgang},
     TITLE = {Periodicity of certain piecewise affine planar maps},
   JOURNAL = {Tsukuba J. Math.},
  FJOURNAL = {Tsukuba Journal of Mathematics},
    VOLUME = {32},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {197--251},
      ISSN = {0387-4982},
   MRCLASS = {37C25 (37E15)},
  MRNUMBER = {MR2433023},
MRREVIEWER = {Peter Ashwin},
}
@comment{arxiv1309.6598}
@article {MR3371156,
    AUTHOR = {de Faria, Jo{\~a}o Alberto and Hutz, Benjamin},
     TITLE = {Combinatorics of cycle lengths on {W}ehler {K}3 surfaces over
              finite fields},
   JOURNAL = {New Zealand J. Math.},
  FJOURNAL = {New Zealand Journal of Mathematics},
    VOLUME = {45},
      YEAR = {2015},
     PAGES = {19--31},
      ISSN = {1171-6096},
   MRCLASS = {37P55},
  MRNUMBER = {3371156},
MRREVIEWER = {Simone Ugolini},
}
@comment{arxiv1509.06670}
@article {MR3846410,
    AUTHOR = {de Faria, Jo\~{a}o Alberto and Hutz, Benjamin},
     TITLE = {Automorphism groups and invariant theory on {$\mathbb{P}^N$}},
   JOURNAL = {J. Algebra Appl.},
  FJOURNAL = {Journal of Algebra and its Applications},
    VOLUME = {17},
      YEAR = {2018},
    NUMBER = {9},
     PAGES = {1850162, 38},
      ISSN = {0219-4988},
   MRCLASS = {37P05 (13A50 37P45)},
  MRNUMBER = {3846410},
       DOI = {10.1142/S0219498818501621},
       URL = {https://doi.org/10.1142/S0219498818501621},
}
@article {MR2990080,
    AUTHOR = {Albeverio, S. and Rozikov, U. A. and Sattarov, I. A.},
     TITLE = {{$p$}-adic {$(2,1)$}-rational dynamical systems},
   JOURNAL = {J. Math. Anal. Appl.},
  FJOURNAL = {Journal of Mathematical Analysis and Applications},
    VOLUME = {398},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {553--566},
      ISSN = {0022-247X},
     CODEN = {JMANAK},
   MRCLASS = {37P05 (11S82)},
  MRNUMBER = {2990080},
MRREVIEWER = {Lingmin Liao},
       DOI = {10.1016/j.jmaa.2012.09.009},
       URL = {http://dx.doi.org/10.1016/j.jmaa.2012.09.009},
}

@article {MR1840304,
    AUTHOR = {Albeverio, S. and Tirotstsi, B. and Khrennikov, A.
              Yu. and de Shmedt, S.},
     TITLE = {{$p$}-adic dynamical systems},
   JOURNAL = {Teoret. Mat. Fiz.},
  FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Teoreticheskaya i
              Matematicheskaya Fizika},
    VOLUME = {114},
      YEAR = {1998},
    NUMBER = {3},
     PAGES = {349--365},
      ISSN = {0564-6162},
   MRCLASS = {37B99 (11S85)},
  MRNUMBER = {MR1840304 (2002a:37018)},
}

@article {MR1928725,
    AUTHOR = {Albeverio, S. and Gundlach, M. and Khrennikov, A. and Lindahl,
              K.-O.},
     TITLE = {On the {M}arkovian behavior of {$p$}-adic random dynamical
              systems},
   JOURNAL = {Russ. J. Math. Phys.},
  FJOURNAL = {Russian Journal of Mathematical Physics},
    VOLUME = {8},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {135--152},
      ISSN = {1061-9208},
   MRCLASS = {60J10 (37H99 81Q99)},
  MRNUMBER = {MR1928725 (2003g:60124)},
MRREVIEWER = {Yves Lacroix},
}

@article {MR2163517,
    AUTHOR = {Ali, Nidal},
     TITLE = {Stabilit\'e des polyn\^omes},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {119},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {53--63},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11R09 (11T06 12E05)},
  MRNUMBER = {MR2163517 (2006h:11125)},
MRREVIEWER = {Peter M{\"u}ller},
}
@comment{The polynomial f is said to be stable if f^m is
irreducible for all positive integers m.}

@comment{UPDATE}
@misc {arxiv0802.2938,
    AUTHOR = {Aliev, Iskander and Smyth, Chris },
    TITLE = {Power maps and subvarieties of the complex algebraic $n$-torus},
     YEAR = {2008},
     NOTE = {\url{arXiv:0802.2938}},
}
@comment{arxiv1610.04271}
@article {MR3757169,
    AUTHOR = {Allen, Kenneth and DeMark, David and Petsche, Clayton},
     TITLE = {Non-{A}rchimedean {H}\'enon maps, attractors, and horseshoes},
   JOURNAL = {Res. Number Theory},
  FJOURNAL = {Research in Number Theory},
    VOLUME = {4},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {Art. 5, 30},
      ISSN = {2363-9555},
   MRCLASS = {37P20 (11S82 37B10 37D45)},
  MRNUMBER = {3757169},
       DOI = {10.1007/s40993-018-0105-2},
       URL = {https://doi.org/10.1007/s40993-018-0105-2},
}
@article {MR292843,
    AUTHOR = {Altman, Allen},
     TITLE = {The size function of abelian varieties},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {164},
      YEAR = {1972},
     PAGES = {153--161},
      ISSN = {0002-9947},
   MRCLASS = {14K10},
  MRNUMBER = {292843},
MRREVIEWER = {T. Ono},
       DOI = {10.2307/1995965},
       URL = {https://doi.org/10.2307/1995965},
}
@comment{arXiv1007.1635}
@article {MR2784670,
    AUTHOR = {Amerik, Ekaterina},
     TITLE = {Existence of non-preperiodic algebraic points for a rational
              self-map of infinite order},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {18},
      YEAR = {2011},
    NUMBER = {2},
     PAGES = {251--256},
      ISSN = {1073-2780},
   MRCLASS = {37Pxx (14Exx)},
  MRNUMBER = {2784670},
}
@article {MR2582437,
     AUTHOR = {Amerik, Ekaterina},
      TITLE = {A computation of invariants of a rational self-map},
    JOURNAL = {Ann. Fac. Sci. Toulouse Math. (6)},
   FJOURNAL = {Annales de la Facult\'e des Sciences de Toulouse.
               Math\'ematiques. S\'erie 6},
     VOLUME = {18},
       YEAR = {2009},
     NUMBER = {3},
      PAGES = {445--457},
       ISSN = {0240-2963},
    MRCLASS = {14E05},
   MRNUMBER = {2582437 (2011b:14031)},
MRREVIEWER = {Marko Roczen},
}
@incollection {MR3477538,
    AUTHOR = {Amerik, Ekaterina},
     TITLE = {Some applications of {$p$}-adic uniformization to algebraic
              dynamics},
 BOOKTITLE = {Rational points, rational curves, and entire holomorphic
              curves on projective varieties},
    SERIES = {Contemp. Math.},
    VOLUME = {654},
     PAGES = {3--21},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2015},
   MRCLASS = {37P55 (14G25)},
  MRNUMBER = {3477538},
MRREVIEWER = {Michelle Ann Manes},
       DOI = {10.1090/conm/654/13213},
       URL = {https://doi.org/10.1090/conm/654/13213},
}
@article {MR2862064,
    AUTHOR = {Amerik, E. and Bogomolov, F. and Rovinsky, M.},
     TITLE = {Remarks on endomorphisms and rational points},
   JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {147},
      YEAR = {2011},
    NUMBER = {6},
     PAGES = {1819--1842},
      ISSN = {0010-437X},
   MRCLASS = {37P55 (11S82 14G05)},
  MRNUMBER = {2862064},
       DOI = {10.1112/S0010437X11005537},
       URL = {http://dx.doi.org/10.1112/S0010437X11005537},
}
@article {MR3424832,
    AUTHOR = {Amerik, Ekaterina and Kurlberg, P\"ar and Nguyen, Khoa D. and
              Towsley, Adam and Viray, Bianca and Voloch, Jos\'e Felipe},
     TITLE = {Evidence for the dynamical {B}rauer-{M}anin criterion},
   JOURNAL = {Exp. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {25},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {54--65},
      ISSN = {1058-6458},
   MRCLASS = {37P15 (11S82 37P05 37P20)},
  MRNUMBER = {3424832},
MRREVIEWER = {Joseph H. Silverman},
       URL = {https://doi.org/10.1080/10586458.2015.1056889},
}
@article {MR1817715,
    AUTHOR = {Amoroso, Francesco and Zannier, Umberto},
     TITLE = {A relative {D}obrowolski lower bound over abelian extensions},
   JOURNAL = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)},
  FJOURNAL = {Annali della Scuola Normale Superiore di Pisa. Classe di
              Scienze. Serie IV},
    VOLUME = {29},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {711--727},
      ISSN = {0391-173X},
     CODEN = {PSNAAI},
   MRCLASS = {11G50 (11J99 11R47)},
  MRNUMBER = {MR1817715 (2003a:11078)},
}
@article {MR1740514,
    AUTHOR = {Amoroso, Francesco and Dvornicich, Roberto},
     TITLE = {A lower bound for the height in abelian extensions},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {80},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {260--272},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11R18 (11G50)},
  MRNUMBER = {MR1740514 (2001b:11100)},
MRREVIEWER = {Christopher Smyth},
}

@incollection {arxiv0602083,
    AUTHOR = {Anashin, Vladimir},
     TITLE = {Ergodic transformations in the space of {$p$}-adic integers},
 BOOKTITLE = {$p$-adic mathematical physics},
    SERIES = {AIP Conf. Proc.},
    VOLUME = {826},
     PAGES = {3--24},
 PUBLISHER = {Amer. Inst. Phys.},
   ADDRESS = {Melville, NY},
      YEAR = {2006},
   MRCLASS = {37A45 (11S85 37A25)},
  MRNUMBER = {MR2258670},
}
@comment{\url{ArXiv:math.math.DS/0602083}}

@article {MR591611,
    AUTHOR = {Anderson, M. and Masser, David W.},
     TITLE = {Lower bounds for heights on elliptic curves},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {174},
      YEAR = {1980},
    NUMBER = {1},
     PAGES = {23--34},
      ISSN = {0025-5874},
   MRCLASS = {10F35 (14G25)},
  MRNUMBER = {591611},
MRREVIEWER = {Daniel Bertrand},
       DOI = {10.1007/BF01215078},
       URL = {https://doi.org/10.1007/BF01215078},
}

@article {arxiv1207.2628,
    AUTHOR = {Anderson, Jacqueline},
     TITLE = {Bounds on the radius of the {$p$}-adic {M}andelbrot set},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {158},
      YEAR = {2013},
    NUMBER = {3},
     PAGES = {253--269},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11S82 (37P05)},
  MRNUMBER = {3040666},
       DOI = {10.4064/aa158-3-5},
       URL = {http://dx.doi.org/10.4064/aa158-3-5},
}
@article {arxiv1610.04969,
    AUTHOR = {Anderson, Jacqueline and Hamblen, Spencer and Poonen, Bjorn
              and Walton, Laura},
     TITLE = {Local arboreal representations},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2018},
    NUMBER = {19},
     PAGES = {5974--5994},
      ISSN = {1073-7928},
   MRCLASS = {11F80 (12F10)},
  MRNUMBER = {3867399},
       DOI = {10.1093/imrn/rnx054},
       URL = {https://doi.org/10.1093/imrn/rnx054},
}
@comment{arxiv1703.08563}
@incollection {MR3882706,
    AUTHOR = {Anderson, Jacqueline and Bouw, Irene I. and Ejder, Ozlem and
              Girgin, Neslihan and Karemaker, Valentijn and Manes, Michelle},
     TITLE = {Dynamical {B}elyi maps},
 BOOKTITLE = {Women in numbers {E}urope {II}},
    SERIES = {Assoc. Women Math. Ser.},
    VOLUME = {11},
     PAGES = {57--82},
 PUBLISHER = {Springer, Cham},
      YEAR = {2018},
   MRCLASS = {37P05 (11G32)},
  MRNUMBER = {3882706},
MRREVIEWER = {Alina Ostafe},
       DOI = {10.1007/978-3-319-74998-3_5},
       URL = {https://doi.org/10.1007/978-3-319-74998-3_5},
}
@comment{UPDATE}
@misc {arxiv2001.10471,
    AUTHOR = {Anderson, Jacqueline and Manes, Michelle and Tobin, Bella},
    TITLE = {Cubic post-critically finite polynomials defined over {$\mathbb{Q}$}},
     YEAR = {2020},
     NOTE = {\url{arXiv:2001.10471}},
}
@comment{UPDATE}
@misc {arxiv2109.03339,
    AUTHOR = {Anderson, Jacqueline and Manes, Michelle and Tobin, Bella},
    TITLE = {Some Applications of Dynamical {B}elyi Polynomials},
     YEAR = {2021},
     NOTE = {\url{arXiv:2109.03339}},
}

@book {MR990016,
    AUTHOR = {Andr{\'e}, Yves},
     TITLE = {{$G$}-functions and geometry},
    SERIES = {Aspects of Mathematics, E13},
 PUBLISHER = {Friedr. Vieweg \& Sohn},
   ADDRESS = {Braunschweig},
      YEAR = {1989},
     PAGES = {xii+229},
      ISBN = {3-528-06317-3},
   MRCLASS = {11J82 (11-02 11G10 11J87 12H25)},
  MRNUMBER = {990016 (90k:11087)},
MRREVIEWER = {C. L. Stewart},
}
@comment{UPDATE}
@misc {arxiv2001.00659,
    AUTHOR = {Andrews, Jesse and Petsche, Clayton},
    TITLE = {Abelian extensions in dynamical {G}alois theory},
     YEAR = {2020},
     NOTE = {\url{arXiv:2001.00659}},
}
@article {MR2220002,
    AUTHOR = {Angl{\`e}s d'Auriac, J.-Ch. and Maillard, J.-M. and Viallet,
              C. M.},
     TITLE = {On the complexity of some birational transformations},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {39},
      YEAR = {2006},
    NUMBER = {14},
     PAGES = {3641--3654},
      ISSN = {0305-4470},
     CODEN = {JPHAC5},
   MRCLASS = {37F10 (14Q99 20F55 37B99)},
  MRNUMBER = {MR2220002 (2006m:37061)},
MRREVIEWER = {Eric Bedford},
}

@book {apostol:utm, 
    AUTHOR = {Apostol, Tom M.},
     TITLE = {Introduction to {A}nalytic {N}umber {T}heory},
      NOTE = {Undergraduate Texts in Mathematics},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1976},
     PAGES = {xii+338},
   MRCLASS = {10-01 (10AXX 10HXX)},
  MRNUMBER = {MR0434929 (55 \#7892)},
MRREVIEWER = {E. Grosswald},
}

@comment{UPDATE}
@misc {arxiv1611.09281,
    AUTHOR = {Arfeux, Matthieu and Kiwi, Jan},
    TITLE = { Irreducibility of the set of cubic polynomials with one
                  periodic critical point},
     YEAR = {2016},
     NOTE = {\url{arXiv:1611.09281}},
}
@comment{arxiv1406.6347}
@article {MR3653089,
    AUTHOR = {Arfeux, Matthieu},
     TITLE = {Dynamics on trees of spheres},
   JOURNAL = {J. Lond. Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {95},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {177--202},
      ISSN = {0024-6107},
   MRCLASS = {37F20},
  MRNUMBER = {3653089},
       DOI = {10.1112/jlms.12016},
       URL = {http://dx.doi.org/10.1112/jlms.12016},
}
@comment{arxiv1408.2117}
@article {MR3645509,
    AUTHOR = {Arfeux, Matthieu},
     TITLE = {Compactification and trees of spheres covers},
   JOURNAL = {Conform. Geom. Dyn.},
  FJOURNAL = {Conformal Geometry and Dynamics. An Electronic Journal of the
              American Mathematical Society},
    VOLUME = {21},
      YEAR = {2017},
     PAGES = {225--246},
      ISSN = {1088-4173},
   MRCLASS = {37F20 (30D05)},
  MRNUMBER = {3645509},
       DOI = {10.1090/ecgd/309},
       URL = {http://dx.doi.org/10.1090/ecgd/309},
}
@comment{arxiv1408.2118}
@article {MR3595486,
    AUTHOR = {Arfeux, Matthieu},
     TITLE = {Approximability of dynamical systems between trees of spheres},
   JOURNAL = {Indiana Univ. Math. J.},
  FJOURNAL = {Indiana University Mathematics Journal},
    VOLUME = {65},
      YEAR = {2016},
    NUMBER = {6},
     PAGES = {1945--1977},
      ISSN = {0022-2518},
   MRCLASS = {37F45},
  MRNUMBER = {3595486},
MRREVIEWER = {David Mart\'\i  Pete},
       DOI = {10.1512/iumj.2016.65.5823},
       URL = {http://dx.doi.org/10.1512/iumj.2016.65.5823},
}
@article {MR2163516,
    AUTHOR = {Arias de Reyna, J.},
     TITLE = {Dynamical zeta functions and {K}ummer congruences},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {119},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {39--52},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11B68 (11A07 11B37 37C30)},
  MRNUMBER = {MR2163516 (2006d:11020)},
MRREVIEWER = {Thomas Ward},
}
	
@book {MR2777369,
    AUTHOR = {Arnol{\cprime}d, V. I.},
     TITLE = {Dynamics, statistics and projective geometry of {G}alois
              fields},
      NOTE = {Translated from the Russian,
              With words about Arnold by Maxim Kazarian and Ricardo
              Uribe-Vargas},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {2011},
     PAGES = {x+80},
      ISBN = {978-0-521-69290-8},
   MRCLASS = {37Pxx (11R32 12E20 37A45)},
  MRNUMBER = {2777369},
}
@article {MR1139553,
    AUTHOR = {Arnol{\cprime}d, V. I.},
     TITLE = {Dynamics of complexity of intersections},
   JOURNAL = {Bol. Soc. Brasil. Mat. (N.S.)},
  FJOURNAL = {Boletim da Sociedade Brasileira de Matem\'atica. Nova S\'erie},
    VOLUME = {21},
      YEAR = {1990},
    NUMBER = {1},
     PAGES = {1--10},
      ISSN = {0100-3569},
   MRCLASS = {58C27 (53C99 57R99 58F14)},
  MRNUMBER = {1139553 (93c:58031)},
MRREVIEWER = {J. S. Joel},
       DOI = {10.1007/BF01236277},
       URL = {http://dx.doi.org/10.1007/BF01236277},
}
@incollection {MR1039340,
    AUTHOR = {Arnol{\cprime}d, V. I.},
     TITLE = {Dynamics of intersections},
 BOOKTITLE = {Analysis, et cetera},
     PAGES = {77--84},
 PUBLISHER = {Academic Press},
   ADDRESS = {Boston, MA},
      YEAR = {1990},
   MRCLASS = {58C35 (57R99 58F15)},
  MRNUMBER = {1039340 (91f:58010)},
MRREVIEWER = {Y. Yomdin},
}
@comment {MR1264116}
@article {arrowsmith:padicsiegeldisk,
    AUTHOR = {Arrowsmith, David K. and Vivaldi, Franco},
     TITLE = {Geometry of {$p$}-adic {S}iegel discs},
   JOURNAL = {Phys. D},
  FJOURNAL = {Physica D. Nonlinear Phenomena},
    VOLUME = {71},
      YEAR = {1994},
    NUMBER = {1-2},
     PAGES = {222--236},
      ISSN = {0167-2789},
     CODEN = {PDNPDT},
   MRCLASS = {11S85 (11S31 58F99)},
  MRNUMBER = {MR1264116 (95d:11162)},
MRREVIEWER = {Evgenii I. Zelenov},
}

@comment {MR1218804}
@article {arrowsmith:padichorseshoe,
    AUTHOR = {Arrowsmith, David K. and Vivaldi, Franco},
     TITLE = {Some {$p$}-adic representations of the {S}male horseshoe},
   JOURNAL = {Phys. Lett. A},
  FJOURNAL = {Physics Letters. A},
    VOLUME = {176},
      YEAR = {1993},
    NUMBER = {5},
     PAGES = {292--294},
      ISSN = {0375-9601},
     CODEN = {PYLAAG},
   MRCLASS = {58F03 (11Z50 32P05)},
  MRNUMBER = {MR1218804 (94c:58054)},
MRREVIEWER = {Evgenii I. Zelenov},
}
@comment{arXiv:1609.02717}
@article {MR4048294,
    AUTHOR = {Astorg, Matthieu},
     TITLE = {Dynamics of post-critically finite maps in higher dimension},
   JOURNAL = {Ergodic Theory Dynam. Systems},
  FJOURNAL = {Ergodic Theory and Dynamical Systems},
    VOLUME = {40},
      YEAR = {2020},
    NUMBER = {2},
     PAGES = {289--308},
      ISSN = {0143-3857},
   MRCLASS = {32H50 (37F10)},
  MRNUMBER = {4048294},
MRREVIEWER = {Jeffrey Diller},
       DOI = {10.1017/etds.2018.32},
       URL = {https://doi.org/10.1017/etds.2018.32},
}
@article {MR4050664,
    AUTHOR = {Auffarth, Robert and Codogni, Giulio},
     TITLE = {Theta divisors whose {G}auss map has a fiber of positive
              dimension},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {548},
      YEAR = {2020},
     PAGES = {153--161},
      ISSN = {0021-8693},
   MRCLASS = {14K25},
  MRNUMBER = {4050664},
MRREVIEWER = {Cherng-tiao Perng},
       DOI = {10.1016/j.jalgebra.2019.11.042},
       URL = {https://doi.org/10.1016/j.jalgebra.2019.11.042},
}
@article {MR3565362,
    AUTHOR = {Auffarth, Robert and Pirola, Gian Pietro and Manni, Riccardo
              Salvati},
     TITLE = {Torsion points on theta divisors},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {145},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {89--99},
      ISSN = {0002-9939},
   MRCLASS = {14K25 (32G20)},
  MRNUMBER = {3565362},
MRREVIEWER = {Rolf Berndt},
       DOI = {10.1090/proc/13230},
       URL = {https://doi.org/10.1090/proc/13230},
}
@article {MR2017146,
    AUTHOR = {Autissier, Pascal},
     TITLE = {Hauteur des correspondances de {H}ecke},
   JOURNAL = {Bull. Soc. Math. France},
  FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France},
    VOLUME = {131},
      YEAR = {2003},
    NUMBER = {3},
     PAGES = {421--433},
      ISSN = {0037-9484},
     CODEN = {BSMFAA},
   MRCLASS = {11G18 (11F32 11G50 14G40)},
  MRNUMBER = {MR2017146 (2004i:11058)},
MRREVIEWER = {Robin de Jong},
}
@comment {\url{ArXiv:math.NT/0404355}}

@article {autissierpreprint04,
    AUTHOR = {Autissier, Pascal},
     TITLE = {Dynamique des correspondances alg\'ebriques et hauteurs},
   JOURNAL = {Int. Math. Res. Not.},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {2004},
    NUMBER = {69},
     PAGES = {3723--3739},
      ISSN = {1073-7928},
   MRCLASS = {14G40 (11G50)},
  MRNUMBER = {MR2099499},
MRREVIEWER = {Robin de Jong},
}
@book {MR1482226,
    AUTHOR = {Axler, Sheldon},
     TITLE = {Linear {A}lgebra {D}one {R}ight},
    SERIES = {Undergraduate Texts in Mathematics},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1997},
     PAGES = {xvi+251},
      ISBN = {0-387-98258-2},
   MRCLASS = {15-01 (47-01)},
  MRNUMBER = {1482226 (98i:15001)},
MRREVIEWER = {K. Chandrasekhara Rao},
}
@article {MR1760091,
    AUTHOR = {Ayad, Mohamed and McQuillan, Donald L.},
     TITLE = {Irreducibility of the iterates of a quadratic polynomial over
              a field},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {93},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {87--97},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11C08 (11R09 11T06 12E10)},
  MRNUMBER = {MR1760091 (2001c:11031)},
MRREVIEWER = {Michel Grandcolas},
}
@article {MR1845367,
    AUTHOR = {Ayad, Mohamed and McQuillan, Donald L.},
     TITLE = {Corrections to: ``{I}rreducibility of the iterates of a
              quadratic polynomial over a field'' [{A}cta {A}rith.\ \textbf{93}
              (2000), no. 1, 87--97]},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {99},
      YEAR = {2001},
    NUMBER = {1},
     PAGES = {97},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11R09 (11T06 12E10)},
  MRNUMBER = {MR1845367 (2002d:11125)},
}

@article {MR1242609,
    AUTHOR = {Ayad, Mohamed},
     TITLE = {P\'eriodicit\'e (mod {$q$}) des suites elliptiques et points
              {$S$}-entiers sur les courbes elliptiques},
   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier},
    VOLUME = {43},
      YEAR = {1993},
    NUMBER = {3},
     PAGES = {585--618},
      ISSN = {0373-0956},
     CODEN = {AIFUA7},
   MRCLASS = {11B50 (11B83 11D25 11G05)},
  MRNUMBER = {MR1242609 (94f:11009)},
MRREVIEWER = {Franck Lepr{\'e}vost},
}

@comment{UPDATE}
@misc {arxiv1210.0042,
    AUTHOR = {Azevedo, Assis and Carvalho, Maria and Machiavelo, Ant{\'o}nio},
    TITLE = {Dynamics of a quasi-quadratic map},
     YEAR = {2012},
     NOTE = {\url{arXiv:1210.0042}},
}

@comment{--BBB-- }

@comment{UPDATE}
@article {MR3067805,
    AUTHOR = {Bach, Eric and Bridy, Andrew},
     TITLE = {On the number of distinct functional graphs of affine-linear
              transformations over finite fields},
   JOURNAL = {Linear Algebra Appl.},
  FJOURNAL = {Linear Algebra and its Applications},
    VOLUME = {439},
      YEAR = {2013},
    NUMBER = {5},
     PAGES = {1312--1320},
      ISSN = {0024-3795},
     CODEN = {LAAPAW},
   MRCLASS = {37P25 (05C20 11T55)},
  MRNUMBER = {3067805},
       DOI = {10.1016/j.laa.2013.04.014},
       URL = {http://dx.doi.org/10.1016/j.laa.2013.04.014},
}
@comment{UPDATE}
@misc {arxiv1201.4503,
    AUTHOR = {Baier, Stephan and Jaidee, Sawian and Stevens, Shaun 
                  and Ward, Thomas },
    TITLE = {Automorphisms with exotic orbit growth},
     YEAR = {2012},
     NOTE = {\url{arXiv:1201.4503}},
}
@comment{UPDATE}
@misc {arxiv1410.0591,
    AUTHOR = {Bajpai, Dvij and Benedetto, Robert and Chen, Ruqian and
                  Kim, Edward and Marschall, Owen and Onul, Darius and
                  Xiao, Yang},
    TITLE = {Non-archimedean connected {J}ulia sets with branching},
     YEAR = {2014},
     NOTE = {\url{arXiv:1410.0591}},
}
@incollection {MR0277001,
    AUTHOR = {Banchoff, Thomas F. and Rosen, Michael I.},
     TITLE = {Periodic points of {A}nosov diffeomorphisms},
 BOOKTITLE = {Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley,
              Calif., 1968)},
     PAGES = {17--21},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, R.I.},
      YEAR = {1970},
   MRCLASS = {57.48 (34.00)},
  MRNUMBER = {MR0277001 (43 \#2738)},
MRREVIEWER = {J. W. Robbin},
}
@article {MR2727656,
    AUTHOR = {Bandman, Tatiana and Grunewald, Fritz and Kunyavski{\u\i},
              Boris},
     TITLE = {Geometry and arithmetic of verbal dynamical systems on simple
              groups},
      NOTE = {With an appendix by Nathan Jones},
   JOURNAL = {Groups Geom. Dyn.},
  FJOURNAL = {Groups, Geometry, and Dynamics},
    VOLUME = {4},
      YEAR = {2010},
    NUMBER = {4},
     PAGES = {607--655},
      ISSN = {1661-7207},
   MRCLASS = {37Pxx (14Gxx 20Gxx)},
  MRNUMBER = {2727656},
       DOI = {10.4171/GGD/98},
       URL = {http://dx.doi.org/10.4171/GGD/98},
}
@article {Bang1886,
    AUTHOR = {Bang, A.S.},
     TITLE = {Taltheoretiske undersolgelser},
   JOURNAL = {Tidskrift f. Math.},
    VOLUME = {5},
      YEAR = {1886},
     PAGES = {70--80 and 130--137},
}
@book {MR1074572,
    AUTHOR = {Baker, Alan},
     TITLE = {Transcendental number theory},
    SERIES = {Cambridge Mathematical Library},
   EDITION = {Second},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {1990},
     PAGES = {x+165},
      ISBN = {0-521-39791-X},
   MRCLASS = {11Jxx (11J81)},
  MRNUMBER = {1074572 (91f:11049)},
}
@article {MR0169989,
    AUTHOR = {Baker, I. N.},
     TITLE = {Fixpoints of polynomials and rational functions},
   JOURNAL = {J. London Math. Soc.},
    VOLUME = {39},
      YEAR = {1964},
     PAGES = {615--622},
   MRCLASS = {30.10},
  MRNUMBER = {MR0169989 (30 \#230)},
MRREVIEWER = {W. J. Thron},
}
@comment{see also Kisaka for representatives of the exceptional maps, and
for characteristic p, see Pezda}

@article {MR1979685,
    AUTHOR = {Baker, Matthew H.},
     TITLE = {Lower bounds for the canonical height on elliptic curves over
              abelian extensions},
   JOURNAL = {Int. Math. Res. Not.},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {2003},
    NUMBER = {29},
     PAGES = {1571--1589},
      ISSN = {1073-7928},
   MRCLASS = {11G50 (11G05)},
  MRNUMBER = {1979685},
MRREVIEWER = {Matthew A. Papanikolas},
       DOI = {10.1155/S1073792803212083},
       URL = {https://doi.org/10.1155/S1073792803212083},
}
@article {MR2355607,
    AUTHOR = {Baker, Matthew and Norine, Serguei},
     TITLE = {Riemann-{R}och and {A}bel-{J}acobi theory on a finite graph},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {215},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {766--788},
      ISSN = {0001-8708},
   MRCLASS = {05C50 (05C25 05C38 14H99)},
  MRNUMBER = {2355607},
MRREVIEWER = {Tatiana Smirnova-Nagnibeda},
       DOI = {10.1016/j.aim.2007.04.012},
       URL = {https://doi.org/10.1016/j.aim.2007.04.012},
}
@comment{UPDATE}
@misc {arxiv0606252,
   AUTHOR = {Baker, Matthew},
    TITLE = {Uniform structures and {B}erkovich spaces},
     YEAR = {2006},
     NOTE = {\url{ArXiv:math.NT/0606252}},
}
@comment{16 pages ? is this ever going to appear?}

@article {arxiv0507484,
    AUTHOR = {Baker, Matthew},
     TITLE = {A lower bound for average values of dynamical {G}reen's
              functions},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {13},
      YEAR = {2006},
    NUMBER = {2-3},
     PAGES = {245--257},
      ISSN = {1073-2780},
   MRCLASS = {14Gxx (11Gxx)},
  MRNUMBER = {MR2231115},
}
@comment{\url{ArXiv:math.NT/0507484}}

@article {arxiv0601046,
    AUTHOR = {Baker, Matthew},
     TITLE = {A finiteness theorem for canonical heights attached to
              rational maps over function fields},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {626},
      YEAR = {2009},
     PAGES = {205--233},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {14Gxx (11G50 11R58)},
  MRNUMBER = {MR2492995},
}
@article {MR2067482,
    AUTHOR = {Baker, Matthew H. and Silverman, Joseph H.},
     TITLE = {A lower bound for the canonical height on abelian varieties
              over abelian extensions},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {11},
      YEAR = {2004},
    NUMBER = {2-3},
     PAGES = {377--396},
      ISSN = {1073-2780},
   MRCLASS = {11G50 (11G10 14K15)},
  MRNUMBER = {2067482},
MRREVIEWER = {Nicolas Ratazzi},
       DOI = {10.4310/MRL.2004.v11.n3.a10},
       URL = {https://doi.org/10.4310/MRL.2004.v11.n3.a10},
}
@article {arxiv0911.0918,
    AUTHOR = {Baker, Matthew and DeMarco, Laura},
     TITLE = {Preperiodic points and unlikely intersections},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {159},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {1--29},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {37P30 (11G50 11S82 37P05 37P35 37P50)},
  MRNUMBER = {2817647 (2012h:37170)},
MRREVIEWER = {Rafe Jones},
       DOI = {10.1215/00127094-1384773},
       URL = {http://dx.doi.org/10.1215/00127094-1384773},
}
@article {arxiv1211.0255,
    AUTHOR = {Baker, Matthew and De Marco, Laura},
     TITLE = {Special curves and postcritically finite polynomials},
   JOURNAL = {Forum Math. Pi},
  FJOURNAL = {Forum of Mathematics. Pi},
    VOLUME = {1},
      YEAR = {2013},
     PAGES = {e3, 35},
      ISSN = {2050-5086},
   MRCLASS = {37F45 (11G50 30C10)},
  MRNUMBER = {3141413},
MRREVIEWER = {Yu Yasufuku},
       DOI = {10.1017/fmp.2013.2},
       URL = {https://doi.org/10.1017/fmp.2013.2},
}

@misc {arxiv0305181,
   AUTHOR = {Baker, Matthew and Hsia, Liang-Chung},
     TITLE = {Canonical heights, transfinite diameters, and polynomial
              dynamics},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {585},
      YEAR = {2005},
     PAGES = {61--92},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11G50 (37A45 37F10)},
  MRNUMBER = {MR2164622 (2006i:11071)},
MRREVIEWER = {Clayton Petsche},
}
@comment{ArXiv:math.NT/0305181, 28 pages}

@article {MR2114791,
    AUTHOR = {Baker, Matthew and Ih, Su-ion},
     TITLE = {Equidistribution of small subvarieties of an abelian variety},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {10},
      YEAR = {2004},
     PAGES = {279--285 (electronic)},
      ISSN = {1076-9803},
   MRCLASS = {11G10 (11G35 14K12 14K15)},
  MRNUMBER = {MR2114791 (2005h:11116)},
MRREVIEWER = {Robin de Jong},
}

@article {arxiv0509485,
    AUTHOR = {Baker, Matthew and Ih, Su-ion and Rumely, Robert},
     TITLE = {A finiteness property of torsion points},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {2},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {217--248},
      ISSN = {1937-0652},
   MRCLASS = {11G50 (11G05 11J71 11J86)},
  MRNUMBER = {MR2377370 (2009g:11078)},
MRREVIEWER = {Clayton Petsche},
}

@comment{UPDATE}
@misc {arxiv0407433,
   AUTHOR = {Baker, Matthew and Rumely, Robert},
    TITLE = {Analysis and dynamics on the {B}erkovich projective line},
     YEAR = {2004},
     NOTE = {\url{ArXiv:math.NT/0407433}},
}
@comment{150 pages, these notes have been subsumed by their book}

@book {bakerrumelyberkbook,
    AUTHOR = {Baker, Matthew and Rumely, Robert},
     TITLE = {Potential theory and dynamics on the {B}erkovich projective
              line},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {159},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2010},
     PAGES = {xxxiv+428},
      ISBN = {978-0-8218-4924-8},
   MRCLASS = {32H50 (14G20 14G22 20F65 31C15 31C45 37Bxx 37Pxx)},
  MRNUMBER = {MR2599526},
}


@comment{UPDATE}
@misc {bakerrumelymontel2005,
   AUTHOR = {Baker, Matthew and Rumely, Robert},
    TITLE = {Montel's theorem for the {B}erkovich projective line and the
                 {B}erkovich {J}ulia set of a rational map},
     YEAR = {2005},
     NOTE = {Preprint},
}
@comment{31 pages ? is this ever going to appear?}

@article {arxiv0407427,
    AUTHOR = {Baker, Matt and Rumely, Robert},
     TITLE = {Harmonic analysis on metrized graphs},
   JOURNAL = {Canad. J. Math.},
  FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de
              Math\'ematiques},
    VOLUME = {59},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {225--275},
      ISSN = {0008-414X},
     CODEN = {CJMAAB},
   MRCLASS = {43A99 (05C12 58C40)},
  MRNUMBER = {MR2310616 (2008h:43019)},
MRREVIEWER = {Charles Favre},
}


@article {arxiv0407426,
   AUTHOR = {Baker, Matthew and Rumely, Robert},
     TITLE = {Equidistribution of small points, rational dynamics, and
              potential theory},
   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier},
    VOLUME = {56},
      YEAR = {2006},
    NUMBER = {3},
     PAGES = {625--688},
      ISSN = {0373-0956},
     CODEN = {AIFUA7},
   MRCLASS = {11G50 (37A45 37F10)},
  MRNUMBER = {MR2244226}, 
}
@comment{ArXiv:math.NT/0407426, 53 pages}

@book {MR2686830,
    AUTHOR = {Baragar, Arthur},
     TITLE = {The {M}arkoff equation and equations of {H}urwitz},
      NOTE = {Thesis (Ph.D.)--Brown University},
 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {1991},
     PAGES = {164},
   MRCLASS = {Thesis},
  MRNUMBER = {2686830},
       URL =
              {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:9204827},
}
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@article {MR2059748,
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@article {MR3654074,
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@comment{UPDATE}
@misc {arxiv2205.05562,
    AUTHOR = {Barroero, Fabrizio and Capuano, Laura and Turchet, Amos},
    TITLE = {Greatest Common Divisor results on semiabelian varieties and a Conjecture of {S}ilverman},
     YEAR = {2022},
     NOTE = {\url{arXiv:2205.05562}},
}
@comment{UPDATE}
@misc {arxiv2108.12405,
    AUTHOR = {Barroero, Fabrizio and K{\"u}hne, Lars and Schmidt, Harry},
    TITLE = {Unlikely Intersections of Curves with Algebraic Subgroups in Semiabelian Varieties},
     YEAR = {2021},
     NOTE = {\url{arXiv:2108.12405}},
}
@misc {arxiv2206.03526,
    AUTHOR = {Barsak{\c c}, Burcu and Sadek, Mohammad},
    TITLE = {Simultaneous Rational Periodic Points of Degree $2$ Rational Maps},
     YEAR = {2022},
     NOTE = {\url{arXiv:2206.03526}},
}
@book {MR2030225,
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@comment{UPDATE}
@misc {arxiv2001.02737,
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@article {MR3990792,
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}
@article {batramorton:algebraicdynamics,
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@article {MR1307583,
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@comment{UPDATE}
@misc {arxiv2107.07583,
    AUTHOR = {Bayer-Fluckiger, Eva},
    TITLE = {Isometries of lattices and automorphisms of {K3} surfaces},
     YEAR = {2021},
     NOTE = {\url{arXiv:2107.07583}},
}
@comment{UPDATE}
@misc {arxiv2209.06698,
    AUTHOR = {Bayer-Fluckiger, Eva},
    TITLE = {Automorphisms of {K3} surfaces, signatures, and isometries of lattices},
     YEAR = {2022},
     NOTE = {\url{arXiv:2209.06698}},
}
@comment{UPDATE}
@misc {arxiv1305.6342,
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@comment {MR1128089}
@book{beardon:gtm, 
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@book {MR1406314,
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@article {MR1225960,
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@inproceedings {arxiv1110.1741,
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@comment{survey article}

@article {MR2677899,
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}
		

@incollection {MR2742672,
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@article {MR2496566,
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@article {MR2449533,
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  MRNUMBER = {MR2449533},
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}
		
@article {MR2428100,
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  MRNUMBER = {MR2428100 (2009c:32033)},
MRREVIEWER = {Julie D{\'e}serti},
}
		

@article  {arxiv0512507,
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    NUMBER = {4},
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      ISSN = {1078-0947},
   MRCLASS = {14E07 (37F10)},
  MRNUMBER = {MR2399446 (2009e:14020)},
MRREVIEWER = {Jeffrey Diller},
}
		

@article {MR2280499,
    AUTHOR = {Bedford, Eric and Kim, Kyounghee},
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   MRCLASS = {32H50 (37B40 37C25 37F10)},
  MRNUMBER = {MR2280499 (2008k:32054)},
MRREVIEWER = {Serge Cantat},
}
		

@article {MR2111418,
    AUTHOR = {Bedford, Eric and Kim, Kyounghee},
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  MRNUMBER = {MR2111418 (2006b:14018)},
MRREVIEWER = {Serge Cantat},
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@article {MR1624646,
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@book {MR1781937,
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     TITLE = {Ergodic {T}heory and {T}opological {D}ynamics 
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    SERIES = {London Mathematical Society Lecture Note Series},
    VOLUME = {269},
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@article {MR2098475,
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  MRNUMBER = {MR2098475 (2005f:11109)},
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@article {MR2225492,
    AUTHOR = {Bell, Jason P.},
     TITLE = {A generalised {S}kolem-{M}ahler-{L}ech theorem for affine
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   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {73},
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       URL = {https://doi.org/10.1112/S002461070602268X},
}
@article {MR3687938,
    AUTHOR = {Bell, Jason P. and Satriano, Matthew and Sierra, Susan J.},
     TITLE = {On a dynamical {M}ordell-{L}ang conjecture for coherent
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   JOURNAL = {J. Lond. Math. Soc. (2)},
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    VOLUME = {96},
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   MRCLASS = {14F05 (11D88)},
  MRNUMBER = {3687938},
       DOI = {10.1112/jlms.12050},
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}
@comment{UPDATE}
@misc {arxiv2210.03152,
    AUTHOR = {Bell, Jason and Ghioca, Dragos},
    TITLE = {Intersections of orbits of self-maps with subgroups in semiabelian varieties},
     YEAR = {2022},
     NOTE = {\url{arXiv:2210.03152}},
}
@comment{UPDATE}
@misc {arxiv2202.06364,
    AUTHOR = {Bell, Jason and Ghioca, Dragos},
    TITLE = {A conjecture strengthening the {Z}ariski dense orbit problem for birational maps of dynamical degree one},
     YEAR = {2022},
     NOTE = {\url{arXiv:2202.06364}},
}
@comment{UPDATE}
@misc {arxiv2205.02644,
    AUTHOR = {Bell, Jason and Ghioca, Dragos},
    TITLE = {A fusion variant of the classical and dynamical {M}ordell--{L}ang conjectures in positive characteristic},
     YEAR = {2022},
     NOTE = {\url{arXiv:2205.02644}},
}
@article {MR3373060,
    AUTHOR = {Bell, Jason Pierre and Ghioca, Dragos and Tucker, Thomas John},
     TITLE = {Applications of {$p$}-adic analysis for bounding periods for
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   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2015},
    NUMBER = {11},
     PAGES = {3576--3597},
      ISSN = {1073-7928},
   MRCLASS = {14G20 (14A10 14J50)},
  MRNUMBER = {3373060},
MRREVIEWER = {Remke Kloosterman},
}
@comment{UPDATE}
@misc {arxiv2103.09994,
    AUTHOR = {Bell, Jason P. and Huang, Keping and Peng, Wayne and Tucker, Thomas J.},
    TITLE = {A {T}its alternative for rational functions},
     YEAR = {2021},
     NOTE = {\url{arXiv:2103.09994}},
}
@article {MR3435801,
    AUTHOR = {Bell, Jason P. and Ghioca, Dragos and Tucker, Thomas J.},
     TITLE = {The dynamical {M}ordell-{L}ang problem for {N}oetherian
              spaces},
   JOURNAL = {Funct. Approx. Comment. Math.},
  FJOURNAL = {Uniwersytet im. Adama Mickiewicza w Poznaniu. Wydzia\l 
              Matematyki i Informatyki. Functiones et Approximatio
              Commentarii Mathematici},
    VOLUME = {53},
      YEAR = {2015},
    NUMBER = {2},
     PAGES = {313--328},
      ISSN = {0208-6573},
   MRCLASS = {37P55 (11G05)},
  MRNUMBER = {3435801},
MRREVIEWER = {Liang-Chung Hsia},
       DOI = {10.7169/facm/2015.53.2.7},
       URL = {https://doi.org/10.7169/facm/2015.53.2.7},
}
@article {arxiv:0808.3266,
    AUTHOR = {Bell, J. P. and Ghioca, D. and Tucker, T. J.},
     TITLE = {The dynamical {M}ordell--{L}ang problem for \'etale maps},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {132},
      YEAR = {2010},
    NUMBER = {6},
     PAGES = {1655--1675},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {14Kxx (37Pxx)},
  MRNUMBER = {2766180},
}
@comment{UPDATE}
@misc {arxiv1310.5775,
    AUTHOR = {Bell, J. P. and Ghioca, D. and Tucker, T. J.},
    TITLE = {Applications of $p$-adic analysis to {B}urnside's problem and
                  {Z}hang's conjecture },
     YEAR = {2013},
     NOTE = {\url{arXiv:1310.5775}},
}
@comment{arxiv1712.02897}
@article {MR4028107,
    AUTHOR = {Bell, Jason and Ghioca, Dragos and Tucker, Thomas},
     TITLE = {Bounding periods of subvarieties of {$(\mathbb{P}^1)^n$}},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {26},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {949--971},
      ISSN = {1073-2780},
   MRCLASS = {14G22 (37P05)},
  MRNUMBER = {4028107},
       DOI = {10.4310/MRL.2019.v26.n4.a1},
       URL = {https://doi.org/10.4310/MRL.2019.v26.n4.a1},
}
@comment{arxiv1401.6659}
@book {MR3468757,
    AUTHOR = {Bell, Jason P. and Ghioca, Dragos and Tucker, Thomas J.},
     TITLE = {The dynamical {M}ordell-{L}ang conjecture},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {210},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2016},
     PAGES = {xiii+280},
      ISBN = {978-1-4704-2408-4},
   MRCLASS = {37-02 (11G25 14A10 37Pxx)},
  MRNUMBER = {3468757},
MRREVIEWER = {Liang-Chung Hsia},
}
@comment{UPDATE}
@misc {arxiv1408.4744,
    AUTHOR = {Bell, Jason and Ghioca, Dragos and Reichstein, Zinovy},
    TITLE = {On a dynamical version of a theorem of {R}osenlicht},
     YEAR = {2014},
     NOTE = {\url{arXiv:1408.4744}},
}
@comment{UPDATE}
@misc {arxiv1610.03858,
    AUTHOR = {Bell, Jason and Ghioca, Dragos and Reichstein, Zinovy and Satriano, Matthew},
    TITLE = {On the {M}edvedev--{S}canlon Conjecture for Minimal Threefolds of Non-Negative {K}odaira Dimension},
     YEAR = {2016},
     NOTE = {\url{arXiv:1610.03858}},
}
@comment{UPDATE}
@misc {arxiv1906.08683,
    AUTHOR = {Bell, Jason and Ghioca, Dragos and Satriano, Matthew},
    TITLE = {Dynamical Uniform Bounds for Fibers and a Gap Conjecture},
     YEAR = {2019},
     NOTE = {\url{arXiv:1906.08683}},
}
@comment{UPDATE}
@misc {arxiv2106.11544,
    AUTHOR = {Bell, Jason and Matsuzawa, Yohsuke and Satriano, Matthew},
    TITLE = {On Dynamical Cancellation},
     YEAR = {2021},
     NOTE = {\url{arXiv:2106.11544}},
}
@comment{MR4205407}
@article {arxiv1907.00675,
    AUTHOR = {Bell, Jason P. and Diller, Jeffrey and Jonsson, Mattias},
     TITLE = {A transcendental dynamical degree},
   JOURNAL = {Acta Math.},
  FJOURNAL = {Acta Mathematica},
    VOLUME = {225},
      YEAR = {2020},
    NUMBER = {2},
     PAGES = {193--225},
      ISSN = {0001-5962},
   MRCLASS = {37P05 (11J81 14E05 32H50 37C35 37F80)},
  MRNUMBER = {4205407},
       DOI = {10.4310/ACTA.2020.v225.n2.a1},
       URL = {https://doi.org/10.4310/ACTA.2020.v225.n2.a1},
}

@comment{UPDATE}
@misc {belldillerjonssonkrieger2021,
    AUTHOR = {Bell, Jason and Diller, Jeffrey and Jonsson, Mattias and Krieger, Holly},
    TITLE = {Birational mpas with transcendental dynamical degree},
     YEAR = {2021},
     NOTE = {\url{arXiv:2107.04113}},
}

@comment{UPDATE}
@misc {arxiv2003.01255,
    AUTHOR = {Bell, Jason P. and Hu, Fei and Satriano, Matthew},
    TITLE = {Height Gap Conjectures, $D$-Finiteness, and Weak Dynamical {M}ordell--{L}ang},
     YEAR = {2020},
     NOTE = {\url{arXiv:2003.01255}},
}
@comment{UPDATE}
@misc {arxiv2005.04281,
    AUTHOR = {Bell, Jason P. and Chen, Shaoshi and Ehsaan, Hossain},
    TITLE = {Rational dynamical systems, {$S$}-units, and {$D$}-finite power series},
     YEAR = {2020},
     NOTE = {\url{arXiv:2005.04281}},
}
@comment{arxiv1806.11054}
@article {MR3940945,
    AUTHOR = {Bell, Jason P. and Ghioca, Dragos},
     TITLE = {Periodic subvarieties of semiabelian varieties and
              annihilators of irreducible representations},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {349},
      YEAR = {2019},
     PAGES = {459--487},
      ISSN = {0001-8708},
   MRCLASS = {37P15 (14 20G15 32H50)},
  MRNUMBER = {3940945},
       DOI = {10.1016/j.aim.2019.04.022},
       URL = {https://doi.org/10.1016/j.aim.2019.04.022},
}
@comment{arxiv1312.5305}
@article {MR3314835,
    AUTHOR = {Bell, Jason P. and Lagarias, Jeffrey C.},
     TITLE = {A {S}kolem-{M}ahler-{L}ech theorem for iterated automorphisms
              of {$K$}-algebras},
   JOURNAL = {Canad. J. Math.},
  FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de
              Math\'{e}matiques},
    VOLUME = {67},
      YEAR = {2015},
    NUMBER = {2},
     PAGES = {286--314},
      ISSN = {0008-414X},
   MRCLASS = {11D45 (11D88 11Y55 14R10)},
  MRNUMBER = {3314835},
MRREVIEWER = {Abderrahmane Nitaj},
       DOI = {10.4153/CJM-2013-048-3},
       URL = {https://doi.org/10.4153/CJM-2013-048-3},
}
@comment{UPDATE}
@misc {arxiv1307.2369,
    AUTHOR = {Bell, Jason and Miles, Richard and Ward, Thomas},
    TITLE = {Towards a Polya--Carlson dichotomy for algebraic dynamics},
     YEAR = {2013},
     NOTE = {\url{arXiv:1307.2369}},
}
@comment{UPDATE}
@misc {arxiv2202.01673,
    AUTHOR = {Bell, Jason and Zhong, Xiao},
    TITLE = {{$p$}-adic interpolation of orbits under rational maps},
     YEAR = {2022},
     NOTE = {\url{arXiv:2202.01673}},
}
@article {MR3681355,
    AUTHOR = {Bellah, Elisa and Garton, Derek and Tannenbaum, Erin and
              Walton, Noah},
     TITLE = {A probabilistic heuristic for counting components of
              functional graphs of polynomials over finite fields},
   JOURNAL = {Involve},
  FJOURNAL = {Involve. A Journal of Mathematics},
    VOLUME = {11},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {169--179},
      ISSN = {1944-4176},
   MRCLASS = {37P05 (05C80 37P25)},
  MRNUMBER = {3681355},
       URL = {https://doi.org/10.2140/involve.2018.11.169},
}
@article {MR1704282,
    AUTHOR = {Bellon, M. P. and Viallet, C.-M.},
     TITLE = {Algebraic entropy},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {204},
      YEAR = {1999},
    NUMBER = {2},
     PAGES = {425--437},
      ISSN = {0010-3616},
     CODEN = {CMPHAY},
   MRCLASS = {37D45 (37A35 37C99 39A12)},
  MRNUMBER = {1704282 (2000f:37040)},
MRREVIEWER = {Remo Badii},
       DOI = {10.1007/s002200050652},
       URL = {http://dx.doi.org/10.1007/s002200050652},
}
@comment{conjectures dynamical degree is an algebraic integer}

@UNPUBLISHED{unpubBenMenahem,
 AUTHOR  = {Ben-Menahem, Shahar},
 TITLE   = {$p$-adic iterations},
 NOTE    = {Preprint, {TAUP} 1627--88, {T}el-{A}viv {University}},
 YEAR    = {1988},
}

@phdthesis{benedetto:thesis, 
    AUTHOR = {Benedetto, Robert L.},
    TITLE = {Fatou components in $p$-adic dynamics},
   SCHOOL = {Brown University},
     YEAR = {1998},
}

@article {MR1981035,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Non-{A}rchimedean holomorphic maps and the {A}hlfors {I}slands
              theorem},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {125},
      YEAR = {2003},
    NUMBER = {3},
     PAGES = {581--622},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {30G06 (12J25 30C25)},
  MRNUMBER = {MR1981035 (2004a:30042)},
MRREVIEWER = {William A. Cherry},
}
@article {MR1941304,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Examples of wandering domains in {$p$}-adic polynomial
              dynamics},
   JOURNAL = {C.~R.~Math. Acad. Sci. Paris},
  FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris},
    VOLUME = {335},
      YEAR = {2002},
    NUMBER = {7},
     PAGES = {615--620},
      ISSN = {1631-073X},
   MRCLASS = {37F10 (12J25 37F50)},
  MRNUMBER = {MR1941304 (2003i:37040)},
MRREVIEWER = {Serge Cantat},
}

@comment{MR2157374}
@article {arxiv0312034,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Wandering domains and nontrivial reduction in
              non-{A}rchimedean dynamics},
   JOURNAL = {Illinois J. Math.},
  FJOURNAL = {Illinois Journal of Mathematics},
    VOLUME = {49},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {167--193 (electronic)},
      ISSN = {0019-2082},
     CODEN = {IJMTAW},
   MRCLASS = {11S85 (37B99 37F10 37F50)},
  MRNUMBER = {MR2157374 (2006e:11185)},
MRREVIEWER = {Charles Favre},
}

@article {arxiv0312029,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Wandering domains in non-{A}rchimedean polynomial dynamics},
   JOURNAL = {Bull. London Math. Soc.},
  FJOURNAL = {The Bulletin of the London Mathematical Society},
    VOLUME = {38},
      YEAR = {2006},
    NUMBER = {6},
     PAGES = {937--950},
      ISSN = {0024-6093},
     CODEN = {LMSBBT},
   MRCLASS = {12J25 (37Bxx 37Fxx)},
  MRNUMBER = {MR2285248},
}

@article {arxiv0510444,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Heights and preperiodic points of polynomials over function
              fields},
   JOURNAL = {Int. Math. Res. Not.},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {2005},
    NUMBER = {62},
     PAGES = {3855--3866},
      ISSN = {1073-7928},
   MRCLASS = {11G50 (11R58)},
  MRNUMBER = {MR2202175},
MRREVIEWER = {Clayton Petsche},
}

@article {MR1863402,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Components and periodic points in non-{A}rchi\-me\-dean dynamics},
   JOURNAL = {Proc. London Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {84},
      YEAR = {2002},
    NUMBER = {1},
     PAGES = {231--256},
      ISSN = {0024-6115},
     CODEN = {PLMTAL},
   MRCLASS = {11S85 (37F10 37F50)},
  MRNUMBER = {MR1863402 (2002k:11215)},
MRREVIEWER = {Michael E. Zieve},
}
@article {MR1864055,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {An elementary product identity in polynomial dynamics},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {108},
      YEAR = {2001},
    NUMBER = {9},
     PAGES = {860--864},
      ISSN = {0002-9890},
     CODEN = {AMMYAE},
   MRCLASS = {11C08 (11R27 13B25 37F10)},
  MRNUMBER = {MR1864055 (2003g:11021)},
MRREVIEWER = {Peter Ha{\"{\i}}ssinsky},
}
@article {benedetto:hyperbolic,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Hyperbolic maps in {$p$}-adic dynamics},
   JOURNAL = {Ergodic Theory Dynam. Systems},
  FJOURNAL = {Ergodic Theory and Dynamical Systems},
    VOLUME = {21},
      YEAR = {2001},
    NUMBER = {1},
     PAGES = {1--11},
      ISSN = {0143-3857},
   MRCLASS = {11S99 (37D99)},
  MRNUMBER = {MR1826658 (2002c:11163)},
MRREVIEWER = {Michael E. Zieve},
}
@article {MR1813109,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Reduction, dynamics, and {J}ulia sets of rational functions},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {86},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {175--195},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11S85 (37F10 37F50)},
  MRNUMBER = {MR1813109 (2001m:11211)},
MRREVIEWER = {Serge Cantat},
}
@article {MR1781331,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {{$p$}-adic dynamics and {S}ullivan's no wandering domains
              theorem},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {122},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {281--298},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {37F10 (11S99 37F50 37F99)},
  MRNUMBER = {MR1781331 (2001f:37054)},
MRREVIEWER = {Serge Cantat},
}

@comment{arxiv0506480}
@article {MR2339471,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Preperiodic points of polynomials over global fields},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {608},
      YEAR = {2007},
     PAGES = {123--153},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11G35 (37Bxx 37F10)},
  MRNUMBER = {MR2339471},
}

@comment{arxiv1311.6695}
@article {MR3263950,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {A criterion for potentially good reduction in nonarchimedean
              dynamics},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {165},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {251--256},
      ISSN = {0065-1036},
   MRCLASS = {37P05 (11S82 37P20)},
  MRNUMBER = {3263950},
       DOI = {10.4064/aa165-3-4},
       URL = {http://dx.doi.org/10.4064/aa165-3-4},
}
@comment{UPDATE}
@misc {arxiv1312.4493,
    AUTHOR = {Benedetto, Robert L.},
    TITLE = {Attaining potentially good reduction in arithmetic dynamics},
     YEAR = {2013},
     NOTE = {\url{arXiv:1312.4493}},
}

@comment{benedettobook}
@book {MR3890051,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Dynamics in one non-archimedean variable},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {198},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2019},
     PAGES = {xviii+463},
      ISBN = {978-1-4704-4688-8},
   MRCLASS = {37-01 (11S82 37Pxx)},
  MRNUMBER = {3890051},
MRREVIEWER = {Michael Louis Tepper},
}
@comment{UPDATE}
@misc {arxiv2201.07868,
    AUTHOR = {Benedetto, Robert L. and Goksel, Vefa},
    TITLE = {Misiurewicz polynomials and dynamical units, Part {I}},
     YEAR = {2022},
     NOTE = {\url{arXiv:2201.07868}},
}

@comment{UPDATE}
@misc {arxiv2203.14431,
    AUTHOR = {Benedetto, Robert L. and Goksel, Vefa},
    TITLE = {Misiurewicz polynomials and dynamical units, Part {II}},
     YEAR = {2022},
     NOTE = {\url{arXiv:2203.14431}},
}

@comment{UPDATE}
@misc {arxiv2005.04656,
    AUTHOR = {Benedetto, Robert L. and Ih, Su-Ion},
    TITLE = {Discreteness of postcritically finite maps in {$p$}-adic moduli space},
     YEAR = {2020},
     NOTE = {\url{arXiv:2005.04656}},
}
@comment{UPDATE}
@misc {arxiv2010.15941,
    AUTHOR = {Benedetto, Robert L. and Ih, Su-Ion},
    TITLE = {A finiteness property of postcritically finite unicritical polynomials},
     YEAR = {2020},
     NOTE = {\url{arXiv:2010.15941}},
}
@comment{arxiv1201.1605}
@article {MR3265554,
    AUTHOR = {Benedetto, Robert and Ingram, Patrick and Jones, Rafe and
              Levy, Alon},
     TITLE = {Attracting cycles in {$p$}-adic dynamics and height bounds for
              postcritically finite maps},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {163},
      YEAR = {2014},
    NUMBER = {13},
     PAGES = {2325--2356},
      ISSN = {0012-7094},
   MRCLASS = {37P20 (37F10 37P45)},
  MRNUMBER = {3265554},
       DOI = {10.1215/00127094-2804674},
       URL = {https://doi.org/10.1215/00127094-2804674},
}
@article {MR2501344,
    AUTHOR = {Benedetto, Robert L. and Dickman, Benjamin and Joseph, Sasha
              and Krause, Benjamin and Rubin, Daniel and Zhou, Xinwen},
     TITLE = {Computing points of small height for cubic polynomials},
   JOURNAL = {Involve},
  FJOURNAL = {Involve. A Journal of Mathematics},
    VOLUME = {2},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {37--64},
   MRCLASS = {11G50 (37F10)},
  MRNUMBER = {MR2501344},
}
@comment{arxiv1312.0491}
@article {MR3277939,
    AUTHOR = {Benedetto, Robert L. and Chen, Ruqian and Hyde, Trevor and
              Kovacheva, Yordanka and White, Colin},
     TITLE = {Small dynamical heights for quadratic polynomials and rational
              functions},
   JOURNAL = {Exp. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {23},
      YEAR = {2014},
    NUMBER = {4},
     PAGES = {433--447},
      ISSN = {1058-6458},
   MRCLASS = {37P35 (11G50 37P30)},
  MRNUMBER = {3277939},
MRREVIEWER = {Michael Louis Tepper},
       DOI = {10.1080/10586458.2014.938203},
       URL = {https://doi.org/10.1080/10586458.2014.938203},
}
@article {
arxiv1806.04980,
    AUTHOR = {Benedetto, Robert and Ingram, Patrick and Jones, Rafe and
              Manes, Michelle and Silverman, Joseph H. and Tucker, Thomas
              J.},
     TITLE = {Current trends and open problems in arithmetic dynamics},
   JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
  FJOURNAL = {American Mathematical Society. Bulletin. New Series},
    VOLUME = {56},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {611--685},
      ISSN = {0273-0979},
   MRCLASS = {37P05 (37P15 37P20 37P25 37P30 37P45 37P55)},
  MRNUMBER = {4007163},
       DOI = {10.1090/bull/1665},
       URL = {https://doi.org/10.1090/bull/1665},
      NOTE = {Article electronically published on March 1, 2019. \url{https://doi.org/10.1090/bull/1665}},
}
@comment {MR2885573}
@article {arXiv:0712.2344,
    AUTHOR = {Benedetto, Robert L. and Ghioca, Dragos and Kurlberg, P{\"a}r
              and Tucker, Thomas J.},
     TITLE = {A case of the dynamical {M}ordell-{L}ang conjecture},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {352},
      YEAR = {2012},
    NUMBER = {1},
     PAGES = {1--26},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {37Pxx (14Gxx)},
  MRNUMBER = {2885573},
       DOI = {10.1007/s00208-010-0621-4},
       URL = {http://dx.doi.org/10.1007/s00208-010-0621-4},
}
@comment{MR2660684}
@article {arXiv0810.1086,
    AUTHOR = {Benedetto, Robert L. and Ghioca, Dragos and Kurlberg, P{\"a}r
              and Tucker, Thomas J.},
     TITLE = {A gap principle for dynamics},
   JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {146},
      YEAR = {2010},
    NUMBER = {4},
     PAGES = {1056--1072},
      ISSN = {0010-437X},
   MRCLASS = {37P55 (14G25 37F10)},
  MRNUMBER = {2660684 (2011m:37155)},
MRREVIEWER = {Patrick Ingram},
       DOI = {10.1112/S0010437X09004667},
       URL = {http://dx.doi.org/10.1112/S0010437X09004667},
}
@article {MR3010142,
    AUTHOR = {Benedetto, Robert L. and Ghioca, Dragos and Hutz, Benjamin and
              Kurlberg, P{\"a}r and Scanlon, Thomas and Tucker, Thomas J.},
     TITLE = {Periods of rational maps modulo primes},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {355},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {637--660},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {37P05 (37P15)},
  MRNUMBER = {3010142},
MRREVIEWER = {Jean-Yves Briend},
       DOI = {10.1007/s00208-012-0799-8},
       URL = {http://dx.doi.org/10.1007/s00208-012-0799-8},
}
@comment{UPDATE}
@misc {arxiv1612.03358,
    AUTHOR = {Benedetto, Robert and Faber, Xander and Hutz, Benjamin
                  and Juul, Jamie and Yasufuku, Yu},
    TITLE = {A large arboreal {G}alois representation for a cubic
                  postcritically finite polynomial},
     YEAR = {2016},
     NOTE = {\url{arXiv:1612.03358}},
}
@article {arxiv1803.01987,
    AUTHOR = {Benedetto, Robert L. and Juul, Jamie},
     TITLE = {Odoni's conjecture for number fields},
   JOURNAL = {Bull. Lond. Math. Soc.},
  FJOURNAL = {Bulletin of the London Mathematical Society},
    VOLUME = {51},
      YEAR = {2019},
    NUMBER = {2},
     PAGES = {237--250},
      ISSN = {0024-6093},
   MRCLASS = {37P05 (11R32 14G25)},
  MRNUMBER = {3937585},
MRREVIEWER = {Simone Ugolini},
       DOI = {10.1112/blms.12225},
       URL = {https://doi.org/10.1112/blms.12225},
}
@comment{UPDATE}
@misc {arxiv2102.05841,
    AUTHOR = {Benedetto, Robert and Lee, Junghun},
    TITLE = {{$J$}-stability in non-archimedean dynamics},
     YEAR = {2021},
     NOTE = {\url{arXiv:2102.05841}},
}
@incollection {arxiv0705.3233,
    AUTHOR = {Bennett, Curtis D. and Mosteig, Edward},
     TITLE = {On the collection of integers that index the fixed points of
              maps on the space of rational functions},
 BOOKTITLE = {Tapas in experimental mathematics},
    SERIES = {Contemp. Math.},
    VOLUME = {457},
     PAGES = {53--67},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2008},
   MRCLASS = {11B83 (11B25)},
  MRNUMBER = {MR2427664},
MRREVIEWER = {John H. Jaroma},
}
@comment{UPDATE}
@misc {arxiv1811.04971,
    AUTHOR = {B{\'e}rczes, Attila and Ostafe, Alina and Shparlinski,
                  Igor E. and Silverman, Joseph H.},
    TITLE = {Multiplicative dependence among iterated values of
                  rational functions modulo finitely generated groups},
     YEAR = {2018},
     NOTE = {\url{arXiv:1811.04971}},
}
@comment{UPDATE}
@misc {arxiv1811.05824,
    AUTHOR = {Berger, Laurent},
    TITLE = {Rigidity and unlikely intersections for formal groups},
     YEAR = {2018},
     NOTE = {\url{arXiv:1811.05824}},
}
@comment{UPDATE}
@misc {arxiv1702.06037,
    AUTHOR = {Berger, Laurent},
    TITLE = {Nonarchimedean dynamical systems and formal groups}, 
     YEAR = {2017},
     NOTE = {\url{arXiv:1702.06037}},
}
@comment{UPDATE}
@misc {arxiv1603.03631,
    AUTHOR = {Berger, Laurent},
    TITLE = {Lubin's conjecture for full $p$-adic dynamical systems},
     YEAR = {2016},
     NOTE = {\url{arXiv:1603.03631}},
}
@comment{UPDATE}
@misc {arxiv1411.7064,
    AUTHOR = {Berger, Laurent},
    TITLE = {Iterate extensions and relative {L}ubin--{T}ate groups},
     YEAR = {2014},
     NOTE = {\url{arXiv:1411.7064}},
}
@comment{UPDATE}
@misc {arxiv1910.05319,
    AUTHOR = {Berger, Laurent},
    TITLE = {The {W}eierstrass preparation theorem and resultants of {$p$}-adic power series},
     YEAR = {2019},
     NOTE = {\url{arXiv:1910.05319}},
}
@book {MR1070709,
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    VOLUME = {33},
 PUBLISHER = {American Mathematical Society},
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MRREVIEWER = {W. Bartenwerfer},
}

@article {MR1259429,
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}

@article {MR1360770,
    AUTHOR = {Berkovich, Vladimir G.},
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    NUMBER = {9},
     PAGES = {1127--1132},
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   MRCLASS = {11G09 (11F85 11S80 22E50)},
  MRNUMBER = {MR1360770 (96h:11053)},
MRREVIEWER = {David Goss},
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@inproceedings {MR1648064,
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  MRNUMBER = {MR1648064 (99h:14026)},
MRREVIEWER = {Annette Werner},
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@article {MR0288104,
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      ISSN = {0002-9890},
   MRCLASS = {12.30},
  MRNUMBER = {MR0288104 (44 \#5302)},
MRREVIEWER = {A. Evyatar},
}

@incollection {MR638731,
    AUTHOR = {Bertrand, Daniel},
     TITLE = {Probl\`emes de transcendance li\'es aux hauteurs sur les
              courbes elliptiques},
 BOOKTITLE = {Mathematics},
    SERIES = {CTHS: Bull. Sec. Sci., {I}II},
     PAGES = {55--63},
 PUBLISHER = {Bib. Nat.},
   ADDRESS = {Paris},
      YEAR = {1981},
   MRCLASS = {10F35 (14K07)},
  MRNUMBER = {638731 (83e:10046)},
MRREVIEWER = {Michel Laurent},
}
@article {MR1360617,
    AUTHOR = {Bertrand, Daniel},
     TITLE = {Minimal heights and polarizations on group varieties},
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  FJOURNAL = {Duke Mathematical Journal},
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      YEAR = {1995},
    NUMBER = {1},
     PAGES = {223--250},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {11G10 (14K05)},
  MRNUMBER = {1360617},
MRREVIEWER = {Yves Andr{\'e}},
       DOI = {10.1215/S0012-7094-95-08009-0},
       URL = {http://dx.doi.org/10.1215/S0012-7094-95-08009-0},
}
@COMMENT{The following appears in Bertrand's article.
page 235, Proposition 3: (i) The Rosatti involution gives the adjoint for the height pairing.
(ii) There is an endomorphism (tensor R) f = f_{D,L} so that h_L(P) = h_D(f(P)).
}
@article {MR1871293,
    AUTHOR = {Berteloot, Fran{\c{c}}ois and Loeb, Jean-Jacques},
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              {L}att\`es de {$\mathbb{P}\sp k$}},
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  FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France},
    VOLUME = {129},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {175--188},
      ISSN = {0037-9484},
     CODEN = {BSMFAA},
   MRCLASS = {32U40 (32H50)},
  MRNUMBER = {MR1871293 (2002k:32063)},
MRREVIEWER = {Mattias Jonsson},
}

@article {MR2051375,
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  FJOURNAL = {Acta Arithmetica},
    VOLUME = {112},
      YEAR = {2004},
    NUMBER = {2},
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      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {37F10 (11S99 37F50 39B12)},
  MRNUMBER = {MR2051375},
MRREVIEWER = {Serge Cantat},
}
@article {MR2031456,
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    VOLUME = {246},
      YEAR = {2004},
    NUMBER = {1-2},
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     CODEN = {MAZEAX},
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  MRNUMBER = {MR2031456 (2005b:37088)},
MRREVIEWER = {Serge Cantat},
}
@article {MR1871284,
    AUTHOR = {B{\'e}zivin, Jean-Paul},
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   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier},
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     CODEN = {AIFUA7},
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  MRNUMBER = {MR1871284 (2002j:37060)},
MRREVIEWER = {Serge Cantat},
}
@article {MR1864626,
    AUTHOR = {B{\'e}zivin, Jean-Paul},
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  MRNUMBER = {MR1864626 (2002j:37059)},
MRREVIEWER = {Serge Cantat},
}
@article {MR1081812,
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  MRNUMBER = {MR1081812 (91k:11017)},
MRREVIEWER = {L. Skula},
}

@article {MR3472915,
    AUTHOR = {Bhargava, Manjul and Ho, Wei},
     TITLE = {Coregular spaces and genus one curves},
   JOURNAL = {Camb. J. Math.},
  FJOURNAL = {Cambridge Journal of Mathematics},
    VOLUME = {4},
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   MRCLASS = {20G05 (14H10 14H52 14L30)},
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MRREVIEWER = {Toshiyuki Tanisaki},
       DOI = {10.4310/CJM.2016.v4.n1.a1},
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}

@comment{arXiv:1312.0898}
@article {MR3519436,
    AUTHOR = {Bhargava, Manjul and Ho, Wei and Kumar, Abhinav},
     TITLE = {Orbit parametrizations for {K}3 surfaces},
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  MRNUMBER = {3519436},
MRREVIEWER = {Alan Matthew Thompson},
       DOI = {10.1017/fms.2016.12},
       URL = {https://doi.org/10.1017/fms.2016.12},
}

@phdthesis{bhatnagar:thesis, 
    AUTHOR = {Bhatnagar, Anupam},
    TITLE = {Points of Canonical Height Zero on Projective Varieties},
   SCHOOL = {CUNY University},
     YEAR = {2010},
}
@article {MR3316459,
    AUTHOR = {Bhatnagar, Anupam},
     TITLE = {The moduli space of totally marked degree two rational maps},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {167},
      YEAR = {2015},
    NUMBER = {3},
     PAGES = {251--260},
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   MRCLASS = {14D20 (14L30 37P45)},
  MRNUMBER = {3316459},
       DOI = {10.4064/aa167-3-3},
       URL = {http://dx.doi.org/10.4064/aa167-3-3},
}
@comment{UPDATE}
@misc {bhatnagarszpiro11,
    AUTHOR = {Bhatnagar, Anupam and Szpiro, Lucien},
    TITLE = {Canonical height zero over function fields},
     YEAR = {2011},
     NOTE = {in preparation},
}
@article {MR2862209,
    AUTHOR = {Bhatnagar, Anupam and Szpiro, Lucien},
     TITLE = {Very ample polarized self maps extend to projective space},
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  FJOURNAL = {Journal of Algebra},
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      YEAR = {2012},
     PAGES = {251--253},
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  MRNUMBER = {2862209},
MRREVIEWER = {Rafe Jones},
       DOI = {10.1016/j.jalgebra.2011.11.010},
       URL = {http://dx.doi.org/10.1016/j.jalgebra.2011.11.010},
}
@article {MR1149891,
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}
@comment{UPDATE}
@misc {arxiv2110.01151,
    AUTHOR = {Billingsley, Tyler Raven},
    TITLE = {An Algorithm for Checking Injectivity of Specialization Maps from Elliptic Surfaces},
     YEAR = {2021},
     NOTE = {\url{arXiv:2110.01151}},
}
@article {MR1863855,
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              numbers},
      NOTE = {With an appendix by M. Mignotte},
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   MRCLASS = {11D59 (11B39 11Y50)},
  MRNUMBER = {MR1863855 (2002j:11027)},
MRREVIEWER = {Yann Bugeaud},
}
@comment{UPDATE}
@misc {arxiv2104.05842,
    AUTHOR = {Binyamini, Gal and Schmidt, Harry and Yafaev, Andrei},
    TITLE = {Lower bounds for Galois orbits of special points on {S}himura varieties: a point-counting approach},
     YEAR = {2021},
     NOTE = {\url{arXiv:2104.05842}},
}
@article {MR0214605,
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  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {74},
      YEAR = {1967},
     PAGES = {274--276},
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  MRNUMBER = {0214605 (35 \#5454)},
MRREVIEWER = {A. Jaeger},
}
@comment{UPDATE}
@misc {arxiv2012.09774,
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    TITLE = {Silverman--{T}ate Height Inequality For Positive Characteristics},
     YEAR = {2020},
     NOTE = {\url{arXiv:2012.09774}},
}
@article {MR3410471,
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@comment{arXiv:1305.1054}
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@book {bombierigubler,
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@incollection {MR1940161,
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  MRNUMBER = {MR2210638},
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@comment{See also
Briscoe, S. - Jimenez, L. - Medina, L.: Asymptotics of a
transformation on the space of rational functions. SIMU 2002, Report.
Briscoe, S. - Jimenez, L. - Manna, D. - Medina, L. - Moll, V.: The
dynamics of a transformation on the space of rational functions. In
preparation.}

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  MRNUMBER = {MR746961 (86b:32031)},
MRREVIEWER = {W. Bartenwerfer},
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@comment {MR1734635}
@article {bosio:roundoff,
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  MRNUMBER = {MR1734635 (2000k:37130)},
MRREVIEWER = {M. L. Blank},
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@comment{Magma}
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@comment{MR2387430}
@article {arxiv0608267,
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@comment{UPDATE}
@misc {arxiv1607.01530,
    AUTHOR = {Bourgain, Jean and Gamburd, Alexander and Sarnak, Peter},
    TITLE = {Markoff surfaces and strong approximation, {1}},
     YEAR = {2016},
     NOTE = {\url{arXiv:1607.01530}},
}
@article {MR3456887,
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  FJOURNAL = {Comptes Rendus Math\'{e}matique. Acad\'{e}mie des Sciences. Paris},
    VOLUME = {354},
      YEAR = {2016},
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     PAGES = {131--135},
      ISSN = {1631-073X},
   MRCLASS = {11G05 (14G15)},
  MRNUMBER = {3456887},
MRREVIEWER = {John L. Boxall},
       DOI = {10.1016/j.crma.2015.12.006},
       URL = {https://doi.org/10.1016/j.crma.2015.12.006},
}
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   AUTHOR = {T. Bousch},
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@comment{UPDATE}
@misc {arxiv1811.10086,
    AUTHOR = {Bouw, Irene and Ejder, Ozlem and Karemaker, Valentijn},
    TITLE = {Dynamical {B}elyi maps and arboreal {G}alois groups},
     YEAR = {2018},
     NOTE = {\url{arXiv:1811.10086}},
}
@article{MR1413570,
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     title = {Une propri{\'e}t{\'e} des hauteurs locales de
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                  ab{\'e}liennes},
   JOURNAL = {J. Th\'eor. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {111--119},
     publisher = {Universit{\'e} Bordeaux I},
     volume = {7},
     number = {1},
     year = {1995},
     language = {fr},
}
@comment{UPDATE}
@misc {arxiv1808.07676,
    AUTHOR = {Boxall, Gareth and Jones, Gareth and Schmidt, Harry},
    TITLE = {Rational values of transcendental functions and arithmetic dynamics},
     YEAR = {2018},
     NOTE = {\url{arXiv:1808.07676}},
}
@article{boyd:mahlermeasure,
    AUTHOR = {Boyd, David W.},
     TITLE = {Mahler's measure and special values of {$L$}-functions},
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      YEAR = {1998},
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   MRCLASS = {11G40 (11R06 11Y35)},
  MRNUMBER = {MR1618282 (99d:11070)},
MRREVIEWER = {Jan Nekov{\'a}{\v{r}}},
}

@comment{UPDATE}
@misc {arxiv1507.02269,
    AUTHOR = {Breen, Benjamin and Jones, Rafe and Occhipinti, Tommy
                  and Yuen, Michelle},
    TITLE = {Wild ramification in a family of low-degree extensions
                  arising from iteration},
     YEAR = {2015},
     NOTE = {\url{arXiv:1507.02269}},
}

@comment{UPDATE}
@misc {arxiv2012.15765,
    AUTHOR = {Bresciani, Giulio},
    TITLE = {On the {Bombieri--Lang} Conjecture over finitely generated fields},
     YEAR = {2020},
     NOTE = {\url{arXiv:2012.15765}},
}
@comment{UPDATE}
@misc {arxiv1906.02654,
    AUTHOR = {Bridy, Andrew and Larson, Matt},
    TITLE = {The {A}rakelov--{Z}hang pairing and {J}ulia sets},
     YEAR = {2019},
     NOTE = {\url{arXiv:1906.02654}},
}


@comment{UPDATE}
@misc {arxiv1306.5267,
    AUTHOR = {Bridy, Andrew},
    TITLE = {The Artin--Mazur Zeta Function of a Lattes Map 
              in Positive Characteristic},
     YEAR = {2013},
     NOTE = {\url{arXiv:1306.5267}},
}

@comment{UPDATE}
@misc {arxiv1202.0362,
    AUTHOR = {Bridy, Andrew},
    TITLE = {Zeta Functions of Polynomial Dynamics on the Algebraic 
               Closure of a Finite Field},
     YEAR = {2012},
     NOTE = {\url{arXiv:1202.0362}},
}
@article {MR2999074,
    AUTHOR = {Bridy, Andrew},
     TITLE = {Transcendence of the {A}rtin-{M}azur zeta function for
              polynomial maps of {$\mathbb{A}^1(\overline{\mathbb{F}}_p)$}},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {156},
      YEAR = {2012},
    NUMBER = {3},
     PAGES = {293--300},
      ISSN = {0065-1036},
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   MRCLASS = {37P05 (11B85)},
  MRNUMBER = {2999074},
       DOI = {10.4064/aa156-3-6},
       URL = {http://dx.doi.org/10.4064/aa156-3-6},
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@article {MR3669394,
    AUTHOR = {Bridy, Andrew and Garton, Derek},
     TITLE = {Dynamically distinguishing polynomials},
   JOURNAL = {Res. Math. Sci.},
  FJOURNAL = {Research in the Mathematical Sciences},
    VOLUME = {4},
      YEAR = {2017},
     PAGES = {Paper No. 13, 17},
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   MRCLASS = {37P05 (11R32 20B35 37P25)},
  MRNUMBER = {3669394},
       URL = {https://doi.org/10.1186/s40687-017-0103-3},
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@comment{UPDATE}
@misc {arxiv1810.00990,
    AUTHOR = {Bridy, Andrew and Doyle, John R. and Ghioca, Dragos and Hsia, Liang-Chung and Tucker, Thomas J.},
    TITLE = {Finite index theorems for iterated {G}alois groups of unicritical polynomials},
     YEAR = {2018},
     NOTE = {\url{arXiv:1810.00990}},
}
@comment{UPDATE}
@misc {arxiv1910.02828,
    AUTHOR = {Bridy, Andrew and Doyle, John R. and Ghioca, Dragos and Hsia, Liang-Chung and Tucker, Thomas J.},
    TITLE = {A question for iterated {G}alois groups in arithmetic dynamics},
     YEAR = {2019},
     NOTE = {\url{arXiv:1910.02828}},
}

@comment{UPDATE}
@misc {arxiv1801.03215,
    AUTHOR = {Bridy, Andrew and Garton, Derek},
    TITLE = {The cycle structure of unicritical polynomials},
     YEAR = {2017},
     NOTE = {\url{arXiv:1801.03215}},
}

@comment{arxiv1605.04376}
@article {MR3703943,
    AUTHOR = {Bridy, Andrew and Tucker, Thomas J.},
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    VOLUME = {182},
      YEAR = {2018},
     PAGES = {296--310},
      ISSN = {0022-314X},
   MRCLASS = {37P05 (11G50 14G25)},
  MRNUMBER = {3703943},
       URL = {https://doi.org/10.1016/j.jnt.2017.06.015},
}
@comment{arxiv1710.02257}
@article {MR3968866,
    AUTHOR = {Bridy, Andrew and Tucker, Thomas J.},
     TITLE = {Finite index theorems for iterated {G}alois groups of cubic
              polynomials},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {373},
      YEAR = {2019},
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   MRCLASS = {37P15 (11G50 11R32 14G25 37P05 37P30)},
  MRNUMBER = {3968866},
       DOI = {10.1007/s00208-018-1670-3},
       URL = {https://doi.org/10.1007/s00208-018-1670-3},
}
@comment{UPDATE}
@misc {arxiv2107.10310,
    AUTHOR = {Bridy, Andrew and Jones, Rafe and Kelsey, Gregory and Lodge, Russell},
    TITLE = {Iterated monodromy groups of rational functions and periodic points over finite fields},
     YEAR = {2021},
     NOTE = {\url{arXiv:2107.10310}},
}
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@article {arxiv1106.4970,
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@comment{UPDATE}
@misc {arxiv0511442,
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@comment{21 pages}
@article {arxiv1204.4967,
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       URL = {http://dx.doi.org/10.1112/S1461157012001131},
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@article {bryksilva05,
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@incollection {MR2508266,
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MRREVIEWER = {Romain Dujardin},
}
@comment{UPDATE}
@misc {bufflpcfup,
    AUTHOR = {Buff, Xavier},
    TITLE = {On postcritically finite unicritical polynomials},
     YEAR = {2017},
     NOTE = {preprint, \url{https://www.math.univ-toulouse.fr/~buff/Preprints/Gleason/Gleason.pdf}},
}
@comment{UPDATE}
@comment{preprint, \url{https://www.math.univ-toulouse.fr/~buff/Preprints/Misiurewicz/Misiurewicz.pdf}}
@misc {buffepsteinkoch2018,
    AUTHOR = {Buff, Xavier and Epstein, A.L. and Koch, Sarah},
    TITLE = {Irreducibility and postcritically finite unicritical polynomials},
     YEAR = {2018},
     NOTE = {\url{arXiv.1806.11221}},
}
@comment{bufflei11}
@incollection {MR3289906,
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   MRCLASS = {37F10},
  MRNUMBER = {3289906},
MRREVIEWER = {Alfredo Poirier},
}
@incollection {MR2508269,
    AUTHOR = {Buff, Xavier and Epstein, Adam and Koch, Sarah and Pilgrim,
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   MRCLASS = {37F30 (30D05)},
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       URL = {http://dx.doi.org/10.1201/b10617-20},
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@comment{UPDATE}
@misc {arxiv1308.5194,
    AUTHOR = {Buium, Alexandru},
    TITLE = {Differential calculus with integers},
     YEAR = {2013},
     NOTE = {\url{arXiv:1308.5194}},
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@article {MR2171197,
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  FJOURNAL = {International Mathematics Research Notices},
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    NUMBER = {31},
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  MRNUMBER = {MR2171197},
       DOI = {10.1155/IMRN.2005.1889},
}
@comment{\url{ArXiv:math.DS/0505037}}

@article {MR1953049,
    AUTHOR = {Bugeaud, Yann and Corvaja, Pietro and Zannier, Umberto},
     TITLE = {An upper bound for the {G}.{C}.{D}.\ of {$a\sp n-1$} and
              {$b\sp n-1$}},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {243},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {79--84},
      ISSN = {0025-5874},
     CODEN = {MAZEAX},
   MRCLASS = {11J25 (11D75)},
  MRNUMBER = {MR1953049 (2004a:11064)},
MRREVIEWER = {Damien Roy},
}
@article {buiumpreprint050704,
    AUTHOR = {Buium, Alexandru and Zimmerman, Ken},
     TITLE = {Differential orbit spaces of discrete dynamical systems},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {580},
      YEAR = {2005},
     PAGES = {201--230},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11Gxx (37Fxx)},
  MRNUMBER = {MR2130591},
}
@comment{UPDATE}
@misc {arxiv1509.01011,
    AUTHOR = {Gil Jos{\'e} Ignacio Burgos and Philippon, Patrice and
                  Rivera-Letelier, Juan and Sombra, Martín },
    TITLE = {The distribution of {G}alois orbits of points of small
                  height in toric varieties},
     YEAR = {2015},
     NOTE = {\url{arXiv:1509.01011}},
}

@comment{arxiv1508.04193}
@article {MR3639698,
    AUTHOR = {Burnette, Charles and Schmutz, Eric},
     TITLE = {Periods of iterated rational functions},
   JOURNAL = {Int. J. Number Theory},
  FJOURNAL = {International Journal of Number Theory},
    VOLUME = {13},
      YEAR = {2017},
    NUMBER = {5},
     PAGES = {1301--1315},
      ISSN = {1793-0421},
   MRCLASS = {11T06 (11N45)},
  MRNUMBER = {3639698},
MRREVIEWER = {Eugenijus Manstavi\v{c}ius},
       DOI = {10.1142/S1793042117500713},
       URL = {https://doi.org/10.1142/S1793042117500713},
}
@book {buse2005,
    AUTHOR = {Bus{\'e}, Laurent},
    TITLE = {Elimination theory in codimension one and applications},
PUBLISHER = {Lecture Notes for the CIMPA-UNESCO-IRAN school in 
              Zanjan, Iran},
     YEAR = {July 9-22, 2005},
 NOTE = {\url{www-sop.inria.fr/galaad/personnel/Laurent.Buse/cours/cimpa.pdf}},
}
@comment{UPDATE}
@misc {arxiv1608.03328,
    AUTHOR = {Bush, Michael and Hindes, Wade and Looper, Nicole},
    TITLE = {Galois groups of iterates of some unicritical polynomials},
     YEAR = {2016},
     NOTE = {\url{arXiv:1608.03328}},
}

@article {MR3894433,
    AUTHOR = {Byszewski, Jakub and Cornelissen, Gunther},
     TITLE = {Dynamics on abelian varieties in positive characteristic},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {12},
      YEAR = {2018},
    NUMBER = {9},
     PAGES = {2185--2235},
      ISSN = {1937-0652},
   MRCLASS = {37P55 (11N45 14G17 14K02 37C25 37C30)},
  MRNUMBER = {3894433},
       DOI = {10.2140/ant.2018.12.2185},
       URL = {https://doi.org/10.2140/ant.2018.12.2185},
}
@misc {arxiv1802.07662,
    AUTHOR = {Byszewski, Jakub and Cornelissen, Gunther and Royals, Robert and Ward, Thomas},
    TITLE = {Dynamics on abelian varieties in positive characteristic},
     YEAR = {2018},
     NOTE = {\url{arXiv:1802.07662}},
}

@comment{UPDATE}
@misc {arxiv2209.00085,
    AUTHOR = {Byszewski, Jakub and Cornelissen, Gunther and Houben, Marc},
    TITLE = {Dynamics of endomorphisms of algebraic groups and related systems},
     YEAR = {2022},
     NOTE = {\url{arXiv:2209.00085}},
}


@comment{arxiv1904.04942}
@incollection {MR4062561,
    AUTHOR = {Byszewski, Jakub and Cornelissen, Gunther and Houben, Marc},
     TITLE = {Dynamically affine maps in positive characteristic},
 BOOKTITLE = {Dynamics: topology and numbers},
    SERIES = {Contemp. Math.},
    VOLUME = {744},
     PAGES = {125--156},
 PUBLISHER = {Amer. Math. Soc., [Providence], RI},
      YEAR = {[2020] \copyright 2020},
   MRCLASS = {37P55 (14K15 37C30)},
  MRNUMBER = {4062561},
       DOI = {10.1090/conm/744/14982},
       URL = {https://doi.org/10.1090/conm/744/14982},
}
@comment{UPDATE}
@misc {arxiv2008.04971,
    AUTHOR = {Byszewski, Jakub and Cornelissen, Gunther and Tijsma, Djurre}, 
    TITLE = {Automata and finite order elements in the {N}ottingham group},
     YEAR = {2020},
     NOTE = {\url{arXiv:2008.04971}},
}

@comment{--CCC-- }

@comment{arxiv1512.03085}
@article {MR3984021,
    AUTHOR = {Cahn, Jordan and Jones, Rafe and Spear, Jacob},
     TITLE = {Powers in orbits of rational functions: cases of an arithmetic
              dynamical {M}ordell-{L}ang conjecture},
   JOURNAL = {Canad. J. Math.},
  FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de
              Math\'{e}matiques},
    VOLUME = {71},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {773--817},
      ISSN = {0008-414X},
   MRCLASS = {37P05 (11G05 37P15)},
  MRNUMBER = {3984021},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.4153/cjm-2018-026-x},
       URL = {https://doi.org/10.4153/cjm-2018-026-x},
}
@comment{UPDATE}
@misc {arxiv2003.12113,
    AUTHOR = {Cai, Julia and Hutz, Benjamin and Mayer, Leo and Weinreich, Max},
    TITLE = {Automorphism Groups of Endomorphisms of {$\mathbb{P}^1(\overline{\mathbb{F}}_p)$}},
     YEAR = {2020},
     NOTE = {\url{arXiv:2003.12113}},
}
@article {callgoldstine:htonprojspace,
   AUTHOR = {Call, Gregory S. and Goldstine, Susan W.},
    TITLE = {Canonical heights on projective space},
  JOURNAL = {J. Number Theory},
 FJOURNAL = {Journal of Number Theory},
   VOLUME = {63},
     YEAR = {1997},
   NUMBER = {2},
    PAGES = {211--243},
}

@article {callsilv:htonvariety,
    AUTHOR = {Call, Gregory S. and Silverman, Joseph H.},
     TITLE = {Canonical heights on varieties with morphisms},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {89},
      YEAR = {1993},
    NUMBER = {2},
     PAGES = {163--205},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11G35 (14G25)},
  MRNUMBER = {MR1255693 (95d:11077)},
MRREVIEWER = {Takeshi Ooe},
}

@article {callsilv:htonk3,
    AUTHOR = {Call, Gregory S. and Silverman, Joseph H.},
     TITLE = {Computing the canonical height on {$K3$} surfaces},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {65},
      YEAR = {1996},
    NUMBER = {213},
     PAGES = {259--290},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {11G35 (14G25 14J28)},
  MRNUMBER = {MR1322885 (96g:11067)},
MRREVIEWER = {Takeshi Ooe},
}
@comment{UPDATE}
@misc {arxiv2204.13461,
    AUTHOR = {Campagna, Francesco and Dill, Gabriel Andreas},
    TITLE = {Around the support problem for {H}ilbert class polynomials},
     YEAR = {2022},
     NOTE = {\url{arXiv:2204.13461}},
}

@article {arxiv0504533,
    AUTHOR = {Canci, Jung Kyu},
     TITLE = {Cycles for rational maps of good reduction outside a
              prescribed set},
   JOURNAL = {Monatsh. Math.},
  FJOURNAL = {Monatshefte f\"ur Mathematik},
    VOLUME = {149},
      YEAR = {2006},
    NUMBER = {4},
     PAGES = {265--287},
      ISSN = {0026-9255},
     CODEN = {MNMTA2},
   MRCLASS = {11G99 (37F10)},
  MRNUMBER = {MR2284648 (2008a:11074)},
MRREVIEWER = {Joseph H. Silverman},
}

@article {arxiv0512338, 
    AUTHOR = {Canci, Jung Kyu},
     TITLE = {Finite orbits for rational functions},
   JOURNAL = {Indag. Math. (N.S.)},
  FJOURNAL = {Koninklijke Nederlandse Akademie van Wetenschappen.
              Indagationes Mathematicae. New Series},
    VOLUME = {18},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {203--214},
      ISSN = {0019-3577},
   MRCLASS = {11G99 (14E05)},
  MRNUMBER = {MR2352676 (2008k:11073)},
MRREVIEWER = {W. Narkiewicz},
}

@article {Canci07,
    AUTHOR = {Canci, Jung Kyu},
     TITLE = {Rational periodic points for quadratic maps},
   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier},
    VOLUME = {60},
      YEAR = {2010},
    NUMBER = {3},
     PAGES = {953--985},
      ISSN = {0373-0956},
     CODEN = {AIFUA7},
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  MRNUMBER = {2680821 (2011i:14045)},
MRREVIEWER = {Yuri Tschinkel},
       URL = {http://aif.cedram.org/item?id=AIF_2010__60_3_953_0},
}
@comment{UPDATE}
@misc {arxiv1505.05168,
    AUTHOR = {Canci, Jung Kyu},
    TITLE = {Good Reduction for endomorphisms of the Projective Line
                  in Terms of the Branch Locus},
     YEAR = {2015},
     NOTE = {\url{arXiv:1505.05168}},
}
@comment{UPDATE}
@misc {arxiv1505.07753,
    AUTHOR = {Canci, Jung Kyu},
    TITLE = {Preperiodic points for rational functions defined over an
                  algebraic function field of characteristic zero},
     YEAR = {2015},
     NOTE = {\url{arXiv:1505.07753}},
}
@comment{arxiv1403.2293}
@article {MR3556260,
    AUTHOR = {Canci, Jung Kyu and Paladino, Laura},
     TITLE = {Preperiodic points for rational functions defined over a
              global field in terms of good reduction},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {144},
      YEAR = {2016},
    NUMBER = {12},
     PAGES = {5141--5158},
      ISSN = {0002-9939},
   MRCLASS = {37P35 (11D45 37P05)},
  MRNUMBER = {3556260},
MRREVIEWER = {Andreas O. Bender},
       URL = {https://doi.org/10.1090/proc/13096},
}
@comment{UPDATE}
@misc {arxiv1601.07293,
    AUTHOR = {Canci, Jung Kyu and Paladino, Laura},
    TITLE = {On preperiodic points of rational functions defined over
                  {$\mathbb F_p(t)$}},
     YEAR = {2016},
     NOTE = {\url{arXiv:1601.07293}},
}
@comment{arxiv1711.04649}
@article {MR3988810,
    AUTHOR = {Canci, Jung Kyu and Troncoso, Sebastian and Vishkautsan,
              Solomon},
     TITLE = {Scarcity of finite orbits for rational functions over a number
              field},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {190},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {221--237},
      ISSN = {0065-1036},
   MRCLASS = {37P05 (11D45 37P35)},
  MRNUMBER = {3988810},
MRREVIEWER = {Dragos Ghioca},
       DOI = {10.4064/aa180210-4-12},
       URL = {https://doi.org/10.4064/aa180210-4-12},
}
@article {MR3656200,
    AUTHOR = {Canci, Jung Kyu and Vishkautsan, Solomon},
     TITLE = {Quadratic maps with a periodic critical point of period 2},
   JOURNAL = {Int. J. Number Theory},
  FJOURNAL = {International Journal of Number Theory},
    VOLUME = {13},
      YEAR = {2017},
    NUMBER = {6},
     PAGES = {1393--1417},
      ISSN = {1793-0421},
   MRCLASS = {37P35 (37P05)},
  MRNUMBER = {3656200},
       URL = {https://doi.org/10.1142/S1793042117500786},
}
@comment{arxiv1604.03965}
@article {MR3885146,
    AUTHOR = {Canci, Jung Kyu and Vishkautsan, Solomon},
     TITLE = {Scarcity of cycles for rational functions over a number field},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
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      YEAR = {2019},
    NUMBER = {1},
     PAGES = {335--356},
      ISSN = {0002-9947},
   MRCLASS = {37P05 (37P35)},
  MRNUMBER = {3885146},
       DOI = {10.1090/tran/7217},
       URL = {https://doi.org/10.1090/tran/7217},
}
@article {arxiv1103.3853,
    AUTHOR = {Canci, Jung Kyu and Peruginelli, Giulio and Tossici, Dajano},
     TITLE = {On some notions of good reduction for endomorphisms of the
              projective line},
   JOURNAL = {Manuscripta Math.},
  FJOURNAL = {Manuscripta Mathematica},
    VOLUME = {141},
      YEAR = {2013},
    NUMBER = {1-2},
     PAGES = {315--331},
      ISSN = {0025-2611},
     CODEN = {MSMHB2},
   MRCLASS = {14H45 (37P05 37P35)},
  MRNUMBER = {3042691},
       DOI = {10.1007/s00229-012-0573-y},
       URL = {http://dx.doi.org/10.1007/s00229-012-0573-y},
}
@article {MR1864630,
    AUTHOR = {Cantat, Serge},
     TITLE = {Dynamique des automorphismes des surfaces {$K3$}},
   JOURNAL = {Acta Math.},
  FJOURNAL = {Acta Mathematica},
    VOLUME = {187},
      YEAR = {2001},
    NUMBER = {1},
     PAGES = {1--57},
      ISSN = {0001-5962},
     CODEN = {ACMAA8},
   MRCLASS = {32H50 (32C30 32Q15 37A35 37F10)},
  MRNUMBER = {MR1864630 (2003h:32026)},
MRREVIEWER = {Eric Bedford},
}
@article {MR2811600,
    AUTHOR = {Cantat, Serge},
     TITLE = {Sur les groupes de transformations birationnelles des
              surfaces},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {174},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {299--340},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {14E07 (14E05 32J15 37F10)},
  MRNUMBER = {2811600 (2012g:14015)},
MRREVIEWER = {Andreas H{\"o}ring},
       DOI = {10.4007/annals.2011.174.1.8},
       URL = {http://dx.doi.org/10.4007/annals.2011.174.1.8},
}
@incollection {arxiv0912.5413,
    AUTHOR = {Cantat, Serge and Chambert-Loir, Antoine},
     TITLE = {Dynamique {$p$}-adique (d'apr\`es les expos\'es de
              {J}ean-{C}hristophe {Y}occoz)},
 BOOKTITLE = {Quelques aspects des syst\`emes dynamiques polynomiaux},
    SERIES = {Panor. Synth\`eses},
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 PUBLISHER = {Soc. Math. France},
   ADDRESS = {Paris},
      YEAR = {2010},
   MRCLASS = {37P20 (37P40)},
  MRNUMBER = {2932436},
MRREVIEWER = {Charles Favre},
}
@comment{UPDATE}
@misc {arxiv2012.01762,
    AUTHOR = {Cantat, Serge and Dujardin, Romain},
    TITLE = {Finite orbits for large groups of automorphisms of projective surfaces},
     YEAR = {2020},
     NOTE = {\url{arXiv:2012.01762}},
}
@comment{UPDATE}
@misc {arxiv1802.08470,
    AUTHOR = {Cantat, Serge and Xie, Junyi},
    TITLE = {On degrees of birational mappings},
     YEAR = {2018},
     NOTE = {\url{arXiv:1802.08470}},
}
@article {MR2649343,
    AUTHOR = {Cantat, Serge and Loray, Frank},
     TITLE = {Dynamics on character varieties and {M}algrange irreducibility
              of {P}ainlev\'{e} {VI} equation},
   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'{e} de Grenoble. Annales de l'Institut Fourier},
    VOLUME = {59},
      YEAR = {2009},
    NUMBER = {7},
     PAGES = {2927--2978},
      ISSN = {0373-0956},
   MRCLASS = {37F75 (20C15 34M55 57M50)},
  MRNUMBER = {2649343},
MRREVIEWER = {Dmitrii Petrovich Novikov},
       URL = {http://aif.cedram.org/item?id=AIF_2009__59_7_2927_0},
}

@article {MR679001,
    AUTHOR = {Cantor, D. C. and Straus, E. G.},
     TITLE = {On a conjecture of {D}. {H}. {L}ehmer},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Polska Akademia Nauk. Instytut Matematyczny. Acta Arithmetica},
    VOLUME = {42},
      YEAR = {1982/83},
    NUMBER = {1},
     PAGES = {97--100},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {12A15 (10F25)},
  MRNUMBER = {MR679001 (84a:12004)},
MRREVIEWER = {Christopher Smyth},
}

@article {MR4401791,
    AUTHOR = {Caporaso, Lucia and Harris, Joe and Mazur, Barry},
     TITLE = {Uniformity of rational points: an up-date and corrections},
   JOURNAL = {Tunis. J. Math.},
  FJOURNAL = {Tunisian Journal of Mathematics},
    VOLUME = {4},
      YEAR = {2022},
    NUMBER = {1},
     PAGES = {183--201},
      ISSN = {2576-7658},
   MRCLASS = {14G05 (14H10)},
  MRNUMBER = {4401791},
       DOI = {10.2140/tunis.2022.4.183},
       URL = {https://doi.org/10.2140/tunis.2022.4.183},
}
		

@article {MR1325796,
    AUTHOR = {Caporaso, Lucia and Harris, Joe and Mazur, Barry},
     TITLE = {Uniformity of rational points},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
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    NUMBER = {1},
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   MRCLASS = {14G05 (11G35)},
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       DOI = {10.1090/S0894-0347-97-00195-1},
       URL = {https://doi.org/10.1090/S0894-0347-97-00195-1},
}
		
@incollection {MR2181874,
    AUTHOR = {Cardona, Gabriel and Quer, Jordi},
     TITLE = {Field of moduli and field of definition for curves of genus 2},
 BOOKTITLE = {Computational aspects of algebraic curves},
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 PUBLISHER = {World Sci. Publ., Hackensack, NJ},
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   MRCLASS = {14H10},
  MRNUMBER = {2181874},
MRREVIEWER = {Tony Shaska},
       DOI = {10.1142/9789812701640_0006},
       URL = {https://doi.org/10.1142/9789812701640_0006},
}

@book{carlesongamelin:complexdynamics, 
    AUTHOR = {Carleson, Lennart and Gamelin, Theodore W.},
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    SERIES = {Universitext: Tracts in Mathematics},
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      YEAR = {1993},
     PAGES = {x+175},
      ISBN = {0-387-97942-5},
   MRCLASS = {30D05 (30C62 39B12 58F23)},
  MRNUMBER = {MR1230383 (94h:30033)},
MRREVIEWER = {Ben Bielefeld},
}
@article {MR0087673,
    AUTHOR = {Carlitz, Leonard},
     TITLE = {The number of points on certain cubic surfaces over a finite
              field},
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     PAGES = {19--21},
   MRCLASS = {10.0X},
  MRNUMBER = {0087673},
MRREVIEWER = {A. L. Whiteman},
}
@article {MR1502458,
    AUTHOR = {Carmichael, R. D.},
     TITLE = {On the numerical factors of the arithmetic forms
              {$\alpha^n\pm\beta^n$}},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
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      ISSN = {0003-486X},
   MRCLASS = {DML},
  MRNUMBER = {1502458},
       URL = {https://doi.org/10.2307/1967797},
}	
@comment{UPDATE}
@misc {arxiv1810.06342,
    AUTHOR = {Carney, Alexander},
    TITLE = {The {H}odge index theorem for arithmetic intersections over function fields},
     YEAR = {2018},
     NOTE = {\url{arXiv:1810.06342}},
}
@comment{UPDATE}
@misc {arxiv2010.07200,
    AUTHOR = {Carney, Alexander},
    TITLE = {Heights and arithmetic dynamics over finitely generated fields},
     YEAR = {2020},
     NOTE = {\url{arXiv:2010.07200}},
}
@comment{UPDATE}
@misc {arxiv2110.07664,
    AUTHOR = {Carney, Alexander},
    TITLE = {Specialization of canonical heights on abelian varieties},
     YEAR = {2021},
     NOTE = {\url{arXiv:2110.07664}},
}

@comment{UPDATE - check the school}
@phdthesis {carneythesis,
    AUTHOR = {Carney, Alexander},
    TITLE = {The arithmetic {H}odge-index theorem and rigidity of
                  algebraic dynamical systems over function fields},
     YEAR = {2018},
   SCHOOL = {Stanford University},
}
@comment{UPDATE}
@misc {arxiv2108.03123,
    AUTHOR = {Carney, Alexander and Hindes, Wade and Tucker, Thomas J.},
    TITLE = {Integral points in orbits in characteristic $p$},
     YEAR = {2021},
     NOTE = {\url{arXiv:2108.03123}},
}
@comment{UPDATE}
@misc {arxiv2110.06496,
    AUTHOR = {Carter, Annie and Lalín, Matilde and Manes, Michelle and Miller, Alison Beth and Mocz, Lucia},
    TITLE = {Two-variable polynomials with dynamical {M}ahler measure zero},
     YEAR = {2021},
     NOTE = {\url{arXiv:2110.06496}},
}
@comment{UPDATE}
@misc {arxiv2204.04101,
    AUTHOR = {Carter, Annie and Lalín, Matilde and Manes, Michelle and Miller, Alison Beth},
    TITLE = {Dynamical {M}ahler Measure: {A} survey and some recent results},
     YEAR = {2022},
     NOTE = {\url{arXiv:2204.04101}},
}
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     PAGES = {xviii+366},
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   MRCLASS = {11Rxx},
  MRNUMBER = {MR911121 (88h:11073)},
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@article {MR0199150,
    AUTHOR = {Cassels, J. W. S.},
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              curves},
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@book {MR1434478,
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@comment{UPDATE}
@misc {arxiv1711.00490,
    AUTHOR = {Castillo Fernandez, Marianela and  Vidaux, Xavier and Videla, Carlos R. },
    TITLE = {Julia {R}obinson numbers and arithmetical dynamic of quadratic polynomials},
     YEAR = {2017},
     NOTE = {\url{arXiv:1711.00490}},
}
@comment{arxiv1610.07077}
@article {MR4074547,
    AUTHOR = {Cerbu, Alois and Gunther, Elijah and Magee, Michael and
              Peilen, Luke},
     TITLE = {The cycle structure of a {M}arkoff automorphism over finite
              fields},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {211},
      YEAR = {2020},
     PAGES = {1--27},
      ISSN = {0022-314X},
   MRCLASS = {37P05 (11D25 20B27 37E99)},
  MRNUMBER = {4074547},
       DOI = {10.1016/j.jnt.2019.09.022},
       URL = {https://doi.org/10.1016/j.jnt.2019.09.022},
}
@comment{UPDATE}
@misc {arxiv1909.07468,
    AUTHOR = {Cerchia, Michael and Rouse, Jeremy},
    TITLE = {Uniform bounds on the image of arboreal {G}alois representations attached to non-{CM} elliptic curves},
     YEAR = {2019},
     NOTE = {\url{arXiv:1909.07468}},
}

@article {MR966870,
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@article {arxiv1210.4127,
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@comment{\url{ArXiv:math.NT/0304023}}
@incollection {arxiv0812.0944, 
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     TITLE = {Th\'eor\`emes d'\'equidistribution pour les syst\`emes
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}
@article {MR2244803,
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     CODEN = {JRMAA8},
   MRCLASS = {14G40 (14G25)},
  MRNUMBER = {MR2244803 (2008b:14040)},
}

@comment{UPDATE}
@misc {arxiv1204.6277,
    AUTHOR = {Chambert-Loir, Antoine},
    TITLE = {Formes diff{\'e}rentielles réelles et courants sur les 
           espaces de {B}erkovich},
     YEAR = {2012},
     NOTE = {\url{arXiv:1204.6277}},
}
@comment{124 pages}

@comment{UPDATE}
@misc {arxiv1904.05630,
    AUTHOR = {Chambert-Loir, Antoine},
    TITLE = {Arakelov geometry, heights, equidistribution, and the {B}ogomolov conjecture},
     YEAR = {2019},
     NOTE = {\url{arXiv:1904.05630}},
}


@comment{UPDATE}
@misc {arxiv0612556,
   AUTHOR = {Chambert-Loir, Antoine and Thuillier, Amaury},
    TITLE = {Formule de {M}ahler et {\'e}quidistribution logarithmique},
     YEAR = {2006},
     NOTE = {\url{ArXiv:math.NT/0612556}},
}
@comment{24 pages}

@article {MR2543659,
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  FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier},
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@comment{arxiv1702.01976}
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@article {MR0004484,
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@comment{UPDATE}
@misc {arxiv1703.08616,
    AUTHOR = {Chaubey, Sneha and Fuchs, Elena and Hines, Robert and Stange, Katherine E.},
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}
@comment{UPDATE}
@misc {arxiv1111.5060,
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@comment{arxiv1608.02177}
@article {MR3690240,
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  MRNUMBER = {3690240},
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@comment{arxiv1608.04146}
@article {MR3834649,
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  MRNUMBER = {3834649},
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@comment{UPDATE - original title was Strong approximation for the {M}arkoff equation}
@misc {arxiv2011.12940,
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     NOTE = {\url{arXiv:2011.12940}},
}
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@article {MR0072877,
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@comment{UPDATE}
@misc {arxiv1904.02195,
    AUTHOR = {Chio, Ivan},
    TITLE = {Chromatic Zeros On Hierarchical Lattices and Equidistribution on Parameter Space},
     YEAR = {2021},
     NOTE = {\url{arXiv:1904.02195}},
}
@comment{UPDATE}
@misc {arxiv1910.12928,
    AUTHOR = {Chlopecki, Anna and Levier-Gomes, Juliano and Peng,
                  Wayne and Shearer, Alex and Towsley, Adam},
    TITLE = {Permutation polynomials: iteration of shift and inversion
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     YEAR = {2019},
     NOTE = {\url{arXiv:1910.12928}},
}
@article {MR3312085,
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  MRNUMBER = {3312085},
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}
@article {MR4008380,
    AUTHOR = {Cho, Ilwoo},
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@article {MR2072394,
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@article {arxivDS0605439,
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@article {MR1721516,
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@phdthesis{coombs:thesis, 
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@book {MR1662447,
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@book {MR1728313,
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@comment{arxiv1308.5895}
@article {MR3323420,
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@comment{UPDATE}
@misc {arxiv2103.11347,
    AUTHOR = {Corvaja, Pietro and Zannier, Umberto},
    TITLE = {Finiteness theorems on elliptical billiards and a variant
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     NOTE = {\url{arXiv:2103.11347}},
}
@comment{arxiv1802.05309}
@article {MR4223436,
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@comment{UPDATE}
@misc {arxiv1909.01253,
    AUTHOR = {Corvaja, Pietro and Demeio, Julian and Masser, David and Zannier, Umberto},
    TITLE = {On the torsion values for sections of an elliptic scheme},
     YEAR = {2019},
     NOTE = {\url{arXiv:1909.01253}},
}


@comment{UPDATE}
@misc {arxiv1811.00113,
    AUTHOR = {Courcy-Ireland, Matthew de and Magee, Michael},
    TITLE = {{K}esten--{M}c{K}ay law for the {M}arkoff surface mod $p$},
     YEAR = {2018},
     NOTE = {\url{arXiv:1811.00113}},
}
@comment{UPDATE}
@misc {arxiv2105.12411,
    AUTHOR = {Courcy-Ireland, Matthew de},
    TITLE = {Non-planarity of {M}arkoff graphs mod $p$},
     YEAR = {2021},
     NOTE = {\url{arXiv:2105.12411}},
}
@comment{UPDATE}
@misc {arxiv1812.07275,
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    TITLE = {Experiments with the {M}arkoff surface},
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     NOTE = {\url{arXiv:1812.07275}},
}
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@comment{Proof that the splitting field of the $n'th$ iterate is
as large as possible (i.e., the full wreath product) for 
all $n\le 5\cdot10^7$.}

@article {MR2197860,
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}
@comment{--DDD-- }
@article {MR26592,
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@article {MR1778843,
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    AUTHOR = {D'Andrea, Carlos and Dickenstein, Alicia},
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@comment{arxiv1505.05814}
@article {MR3885175,
    AUTHOR = {D'Andrea, Carlos and Ostafe, Alina and Shparlinski, Igor E.
              and Sombra, Mart\'{i}n},
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@comment{UPDATE}
@misc {arxiv1810.09094,
    AUTHOR = {Dang, Nguyen-Bac},
    TITLE = {Degree growth for tame automorphisms of an affine quadric threefold},
     YEAR = {2018},
     NOTE = {\url{arXiv:1810.09094}},
}
@comment{UPDATE}
@misc {arxiv:1701.07760,
    AUTHOR = {Dang, Nguyen-Bac},
    TITLE = {Degrees of Iterates of Rational Maps on Normal Projective Varieties},
     YEAR = {2018},
     NOTE = {\url{arXiv:1701.07760}},
}

@comment{UPDATE}
@misc {arxiv1906.11188,
    AUTHOR = {Dang, Nguyen-Bac and Ghioca, Dragos and Hu, Fei and Lesieutre, John and Satriano, Matthew},
    TITLE = {Higher arithmetic degrees of dominant rational self-maps},
     YEAR = {2019},
     NOTE = {\url{arXiv:1906.11188}},
}

@comment{UPDATE}
@misc {arxiv1905.05026,
    AUTHOR = {Nguyen-Bac Dang and Rohini Ramadas},
    TITLE = {Dynamical invariants of toric correspondences},
     YEAR = {2019},
     NOTE = {\url{arXiv:1905.05026}},
}
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@comment{UPDATE}
@misc {arxiv2202.07142,
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@COMMENT{debesdouai:fldofmod}
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  MRNUMBER = {MR1443489 (98k:11081)},
MRREVIEWER = {Katherine F. Stevenson},
}

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@article {MR3531361,
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@article {MR1981611,
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@article {arxiv0412438,
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@comment{\url{ArXiv:math.DS/0412438}}
 
@article {arxiv0403078,
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@comment{\url{ArXiv:math.DS/0403078}}

@comment{arxiv1607.04471}
@article {MR3831028,
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}
@comment{arxiv1602.05614}
@article {MR3989127,
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  MRNUMBER = {3989127},
       DOI = {10.1017/etds.2017.131},
       URL = {https://doi.org/10.1017/etds.2017.131},
}
@comment{UPDATE}
@misc {arxiv1901.09945,
    AUTHOR = {DeMarco, Laura and Krieger, Holly and Ye, Hexi},
    TITLE = {Uniform {M}anin--{M}umford for a family of genus 2 curves},
     YEAR = {2019},
     NOTE = {\url{arXiv:1901.09945}},
}
@comment{UPDATE}
@misc {arxiv1911.02458,
    AUTHOR = {DeMarco, Laura and Krieger, Holly and Ye, Hexi},
    TITLE = {Common preperiodic points for quadratic polynomials},
     YEAR = {2019},
     NOTE = {\url{arXiv:1911.02458}},
}

@comment{UPDATE}
@misc {arxiv1703.05365,
    AUTHOR = {DeMarco, Laura and Ghioca, Dragos and Krieger, Holly and Nguyen, Khoa and Tucker, Thomas and Ye, Hexi},
    TITLE = {Bounded height in families of dynamical systems},
     YEAR = {2017},
     NOTE = {\url{arXiv:1703.05365}},
}
@comment{UPDATE}
@misc {arxiv2107.05982,
   AUTHOR = {DeMarco, Laura and Mavraki, Niki Myrto},
    TITLE = {Variation of Canonical Height on {$\mathbb{P}^1$} for Fatou points},
     YEAR = {2021},
     NOTE = {\url{arXiv:2107.05982}},
}
@comment{UPDATE}
@misc {arxiv1701.07947,
   AUTHOR = {DeMarco, Laura and Mavraki, Niki Myrto},
    TITLE = {Variation of canonical height and equidistribution},
     YEAR = {2017},
     NOTE = {\url{arXiv:1701.07947}},
}
@comment{UPDATE}
@misc {arxiv2012.14529,
   AUTHOR = {DeMarco, Laura and Mavraki, Niki Myrto},
    TITLE = {Elliptic surfaces and arithmetic equidistribution for $\mathbb{R}$-divisors on curves},
     YEAR = {2020},
     NOTE = {\url{arXiv:2012.14529}},
}
@article {arxiv0601109,
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@article {MR2735763,
    AUTHOR = {DeMarco, Laura and Pilgrim, Kevin},
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  FJOURNAL = {Advances in Mathematics},
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}
@comment{UPDATE}
@misc {arxiv1311.1792,
    AUTHOR = {DeMarco, Laura and Wang, Xiaoguang and Ye, Hexi},
    TITLE = {Torsion points and the {L}att{\`e}s family},
     YEAR = {2013},
     NOTE = {\url{arXiv:1311.1792}},
}

@comment{UPDATE}
@misc {DHJMS2019,
    AUTHOR = {DeMark, David and Hindes, Wade and Jones, Rafe and Misplon, Moses and Stoneman, Michael},
    TITLE = {Eventually stable quadratic polynomials over $\mathbb{Q}$},
     YEAR = {2019},
     NOTE = {\url{arXiv:1902.09220}},
}

@comment{UPDATE}
@misc {arxivNT0605724,
    AUTHOR = {Deninger, Christopher},
    TITLE = {A dynamical systems analogue of {L}ichtenbaum's conjectures 
          on special values of {H}asse-{W}eil zeta functions},
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     NOTE = {\url{ArXiv:math.NT/0605724}},
   MRCLASS = {11R42},
}

@article {arxivDS0608539,
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  FJOURNAL = {Journal of the American Mathematical Society},
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MRREVIEWER = {Thomas Ward},
}
@comment{Includes p-adic analogues of multivariable Mahler measures.}

@incollection {MR1936368,
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@incollection {MR1724887,
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@inproceedings {denniger:foliatedspaces,
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@article {MR1415320,
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@misc {arxiv0505354,
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     NOTE = {unpublished, \url{ArXiv:math.NT/0505354}},
}

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MRREVIEWER = {Franz Halter-Koch},
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@comment{arxiv0909.4130}
@book{devaney:dynamicsbook, 
   AUTHOR = {R. Devaney},
    TITLE = {An Introduction to Chaotic Dynamical Systems},
  EDITION = {2nd},
PUBLISHER = {Addison-Wesley},
  ADDRESS = {Redwood City, CA},
     YEAR = {1989}
	}

@article {MR2776927,
    AUTHOR = {Diao, Hansheng and Silva, Cesar E.},
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              {$p$}-adic numbers},
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       URL = {http://dx.doi.org/10.1134/S2070046611010031},
}
@comment{UPDATE}
@misc {BrDik2012,
    AUTHOR = {Dikranjan, Dikran and Giordano Bruno, Anna},
    TITLE = {Discrete dynamical systems in group theory},
     YEAR = {2012},
     NOTE = {preprint, to appear in the
           Proceedings of a Workshop on Infinite Groups},
}
@comment{UPDATE}
@incollection {BrDik2011,
    AUTHOR = {Dikranjan, Dikran and Giordano Bruno, Anna},
     TITLE = {Topological Entropy and Algebraic Entropy for 
                      group endomorphisms},
 BOOKTITLE = {Proceedings ICTA2011},
      NOTE = {Islamabad, Pakistan, July 4--10, 2011},
 PUBLISHER = {Cambridge Scientific Publishers},
      YEAR = {2012},
}
@comment{Are the two papers, above and below, the same?}
@comment{UPDATE}
@misc {arxiv1308.4019,
    AUTHOR = {Dikranjan, Dikran and Giordano Bruno, Anna},
     TITLE = {Topological Entropy and Algebraic Entropy for 
                      group endomorphisms},
     YEAR = {2013},
     NOTE = {\url{arXiv:1308.4019}},
}

@comment{UPDATE}
@misc {BrDikVir2012,
    AUTHOR = {Dikranjan, Dikran and Giordano Bruno, Anna and Virili, Simone},
    TITLE = {A uniform approach to chaos},
     YEAR = {2012},
     NOTE = {preprint},
}
@article {MR2491886,
    AUTHOR = {Dikranjan, Dikran and Goldsmith, Brendan and Salce, Luigi and
              Zanardo, Paolo},
     TITLE = {Algebraic entropy for abelian groups},
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  FJOURNAL = {Transactions of the American Mathematical Society},
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}
@article {MR1867314,
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}
@comment{UPDATE}
@misc {arxiv1311.4133,
    AUTHOR = {Dimitrov, Vesselin},
    TITLE = {A lower bound on the orbit growth of a regular self-map
                  of affine space},
     YEAR = {2013},
     NOTE = {\url{arXiv:1311.4133}},
}
@comment{UPDATE}
@misc {arxiv1511.04061,
    AUTHOR = {Dimitrov, Vesselin},
    TITLE = {Silverman's conjecture for additive polynomial mappings},
     YEAR = {2015},
     NOTE = {\url{arXiv:1511.04061}},
}
@misc {arXiv:1611.04664,
    AUTHOR = {Dimitrov, Vesselin},
     TITLE = {Convergence to the Mahler measure and the distribution
                  of periodic points for algebraic Noetherian
                  {$\mathbb{Z}^d$}-actions},
      YEAR = {2016},
      NOTE = {\url{arXiv:1611.04664}},
}
@comment{UPDATE}
@misc {arxiv1909.06051,
    AUTHOR = {Dimitrov, Vesselin and Habegger, Philipp},
    TITLE = {Galois orbits of torsion points near atoral sets},
     YEAR = {2019},
     NOTE = {\url{arXiv:1909.06051}},
}
@comment{UPDATE}
@misc {arxiv2001.10276,
    AUTHOR = {Dimitrov, Vesselin and Gao, Ziyang and Habegger, Philipp},
    TITLE = {Uniformity in {M}ordell--{L}ang for curves},
     YEAR = {2020},
     NOTE = {\url{arXiv:2001.10276}},
} 
@comment{UPDATE}
@misc {arxiv2103.07955,
    AUTHOR = {Ding, Zhiguo and Zieve, Michael E.},
    TITLE = {A new family of exceptional rational functions},
     YEAR = {2021},
     NOTE = {\url{arXiv:2103.07955}},
}
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@article {MR2180409,
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@article {MR2056545,
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@comment{UPDATE}
@misc {arxiv2012.03076,
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     YEAR = {2020},
     NOTE = {\url{arXiv:2012.03076}},
}
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@misc{hep-th/0501235,
    title = {{Algebraic geometry of discrete dynamics. The case of one
        variable}},
    author = {Dolotin, V. and Morozov, A.},
    howpublished = {ITEP-TH-02/05},
    eprint = {arXiv:hep-th/0501235},
}
@comment{arxiv1009.3971}
@article {MR2955527,
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@comment{UPDATE}
@misc {arxiv2009.10572,
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@misc {DouHubNotes,
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@comment{UPDATE}
@misc {arxiv1801.09003,
    AUTHOR = {Doyle, John R.},
    TITLE = {Preperiodic points for quadratic polynomials over
                  cyclotomic quadratic fields},
     YEAR = {2018},
     NOTE = {\url{arXiv:1801.09003}},
}
@comment{UPDATE}
@misc {arxiv1509.07098,
    AUTHOR = {Doyle, John R.},
    TITLE = {Preperiodic points for quadratic polynomials with small
                  cycles over quadratic fields},
     YEAR = {2015},
     NOTE = {\url{arXiv:1509.07098}},
}
@comment{arXiv:1501.06821}
@article {MR3487222,
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@article {arxiv1603.08138,
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@comment{MR3937306}
@article {doyle17dynmod,
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@comment{MR4000512}
@article {arxiv1703.04172,
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@misc {arxiv1507.03535,
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     YEAR = {2015},
     NOTE = {\url{arXiv:1507.03535}},
}

@comment{UPDATE}
@misc {arxiv2108.09333,
    AUTHOR = {Doyle, John R. and Fili, Paul and Hyde, Trevor},
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     YEAR = {2021},
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}
@comment{UPDATE}
@misc {arxiv2201.11707,
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    TITLE = {Polynomials with many rational preperiodic points},
     YEAR = {2022},
     NOTE = {\url{arXiv:2201.11707}},
}
@comment{arxiv1309.6401}
@article {MR3218788,
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@misc {arxiv2203.06205,
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}
@comment{MR4065068}
@article {arxiv1711.04233,
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@comment{moduliportrait2017}
@article {MR4132597,
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@comment{fomfodPN2018}
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@comment{UPDATE}
@misc {arxiv1805.05632,
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@comment{--EEE-- }

@article {MR2079832,
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@incollection {MR2044517,
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@article {MR1876275,
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@article {MR1777892,
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@article {MR4047549,
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@comment{UPDATE}
@misc {arxiv2201.09005,
    AUTHOR = {Ejder, Ozlem},
    TITLE = {Arithmetic Monodromy Groups of Dynamical {B}elyi maps},
     YEAR = {2022},
     NOTE = {\url{arXiv:2201.09005}},
}
@misc {elkies:lowhtpts,
   AUTHOR = {Elkies, Noam},
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            $\mathbb{Q}$},
     YEAR = {2002},
     NOTE = {\url{www.math.harvard.edu/~elkies/low_height.html}}
}

@MISC {MO73537,    
   AUTHOR = {Elkies, Noam},
    TITLE = {Closed but not rational points of a real cubic},    
    HOWPUBLISHED = {MathOverflow},    
    NOTE = {\url{http://mathoverflow.net/questions/73537} 
              (version: 2011-08-24)},    
    EPRINT = {http://mathoverflow.net/questions/73537},    
    URL = {http://mathoverflow.net/questions/73537},    
}
@comment{UPDATE}
@misc {arxiv2109.01043,
    AUTHOR = {Jordan S. Ellenberg and Brian Lawrence and Akshay Venkatesh},
    TITLE = {Sparsity of Integral Points on Moduli Spaces of Varieties},
     YEAR = {2021},
     NOTE = {\url{arXiv:2109.01043}},
}
@comment{UPDATE}
@misc {arxiv0910.5704,
    AUTHOR = {Elsawy, Ahmed Noubi},
    TITLE = {Generalization of Some Arithmetical Properties of
        {F}ermat--{E}uler Dynamical Systems},
     YEAR = {2009},
     NOTE = {\url{arXiv:0910.5704}},
}
@comment{UPDATE}
@misc {espteinvideos1994,
    AUTHOR = {Epstein, Adam},
    TITLE = {Two videos on Transversality},
     YEAR = {1994},
     NOTE = {\url{https://www.math.sunysb.edu/Videos/Einstein/video_4x3.php?f=406-19940913-Epstein}, \url{https://www.math.sunysb.edu/Videos/Einstein/video_4x3.php?f=406B-19940913-Epstein}},
}
@book {MR2690048,
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 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
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@article {arxiv1010.2780,
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       URL = {http://dx.doi.org/10.1112/blms/bdr059},
}
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@incollection {MR1084181,
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  MRNUMBER = {MR1084181 (92a:11113)},
MRREVIEWER = {Tian Xin Cai},
}
@article {ErdosTuran1,
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    VOLUME = {I},
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     PAGES = {101--103},
}   
@article {ErdosTuran2,
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}
@article {MR1027462,
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  MRNUMBER = {MR1027462 (90m:30030)},
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}
@article {MR2731707,
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MRREVIEWER = {Min Ru},
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}
@article {MR2833563,
    AUTHOR = {Eremenko, Alexandre and van Strien, Sebastian},
     TITLE = {Rational maps with real multipliers},
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  MRNUMBER = {2833563},
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       URL = {http://dx.doi.org/10.1090/S0002-9947-2011-05308-0},
}
@article {MR1783650,
    AUTHOR = {Everest, Graham and Pinner, Chris},
     TITLE = {Corrigendum: ``{B}ounding the elliptic {M}ahler measure.
              {II}'' [{J}. {L}ondon {M}ath. {S}oc. (2) \textbf{58} (1998), no.
              1, 1--8.]},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
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     CODEN = {JLMSAK},
   MRCLASS = {11G50 (11G05 11R09)},
  MRNUMBER = {MR1783650 (2001g:11103)},
MRREVIEWER = {Yann Bugeaud},
}
@article {MR1666050,
    AUTHOR = {Everest, Graham and Pinner, Chris},
     TITLE = {Bounding the elliptic {M}ahler measure. {II}},
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MRREVIEWER = {Yann Bugeaud},
}
@article {MR1373343,
    AUTHOR = {Everest, Graham and Fhlath{\'u}in, Br{\'{\i}}d N\'\i},
     TITLE = {The elliptic {M}ahler measure},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
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    NUMBER = {1},
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   MRCLASS = {11G05 (11C08 11J99)},
  MRNUMBER = {MR1373343 (97e:11064)},
MRREVIEWER = {Gregory S. Call},
}
@article {everest:ellipticjensen,
   AUTHOR = {Everest, Graham},
    TITLE = {On the elliptic analogue of {J}ensen's formula},
  JOURNAL = {J. London Math. Soc. (2)},
 FJOURNAL = {The Journal of the London Mathematical Society. Second Series},
   VOLUME = {59},
     YEAR = {1999},
   NUMBER = {1},
    PAGES = {21--36},
}
@book {everestward:dynamicsbook,
   AUTHOR = {Everest, Graham and Ward, Thomas},
    TITLE = {Heights of polynomials and entropy in algebraic dynamics},
PUBLISHER = {Springer-Verlag London Ltd.},
  ADDRESS = {London},
     YEAR = {1999},
    PAGES = {xii+211},
}
@article {arxiv0705.1067,
    AUTHOR = {Everest, G. and Miles, R. and Stevens, S. and Ward, T.},
     TITLE = {Dirichlet series for finite combinatorial rank dynamics},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {362},
      YEAR = {2010},
    NUMBER = {1},
     PAGES = {199--227},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {37B99 (11N45 37A45 37B40 37C25 37C35 37P99)},
  MRNUMBER = {2550149 (2011c:37038)},
MRREVIEWER = {Michael E. Zieve},
       DOI = {10.1090/S0002-9947-09-04962-9},
       URL = {http://dx.doi.org/10.1090/S0002-9947-09-04962-9},
}
@article {everestward:dynamicalheight,
   AUTHOR = {Everest, Graham and Ward, Thomas},
    TITLE = {A dynamical interpretation of the global canonical height on an
             elliptic curve},
  JOURNAL = {Experiment. Math.},
 FJOURNAL = {Experimental Mathematics},
   VOLUME = {7},
     YEAR = {1998},
   NUMBER = {4},
    PAGES = {305--316},
}

@article {MR1938222,
    AUTHOR = {Everest, Graham and van der Poorten, Alf and Puri, Yash
              and Ward, Thomas},
     TITLE = {Integer sequences and periodic points},
   JOURNAL = {J. Integer Seq.},
  FJOURNAL = {Journal of Integer Sequences},
    VOLUME = {5},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {Article 02.2.3, 10 pp. (electronic)},
      ISSN = {1530-7638},
   MRCLASS = {11B37 (11B68 37B10 39A10)},
  MRNUMBER = {MR1938222 (2003j:11014)},
MRREVIEWER = {Ali Messaoudi},
}
@book {MR1990179,
    AUTHOR = {Everest, Graham and van der Poorten, Alf and Shparlinski, Igor
              and Ward, Thomas},
     TITLE = {Recurrence {S}equences},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {104},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2003},
     PAGES = {xiv+318},
      ISBN = {0-8218-3387-1},
   MRCLASS = {11B37 (11B85 11G05 11J71 11K45 11T23 37B15 94A60)},
  MRNUMBER = {MR1990179 (2004c:11015)},
MRREVIEWER = {Yann Bugeaud},
}
@article {MR766298,
    AUTHOR = {Evertse, Jan-Hendrik},
     TITLE = {On sums of {$S$}-units and linear recurrences},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {53},
      YEAR = {1984},
    NUMBER = {2},
     PAGES = {225--244},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11J13 (11B37 11J86 11R27)},
  MRNUMBER = {766298 (86c:11045)},
MRREVIEWER = {T. N. Shorey},
}


@comment{--FFF-- }

@article {MR2506588,
    AUTHOR = {Faber, X. W. C.},
     TITLE = {Equidistribution of dynamically small subvarieties over the
              function field of a curve},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {137},
      YEAR = {2009},
    NUMBER = {4},
     PAGES = {345--389},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {14Gxx (11G35)},
  MRNUMBER = {MR2506588},
       DOI = {10.4064/aa137-4-4},
       URL = {http://dx.doi.org/10.4064/aa137-4-4},
}
@article {arxiv0907.4365,
    AUTHOR = {Faber, X. W. C.},
     TITLE = {A remark on the effective {M}ordell conjecture and rational
              pre-images under quadratic dynamical systems},
   JOURNAL = {C. R. Math. Acad. Sci. Paris},
  FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris},
    VOLUME = {348},
      YEAR = {2010},
    NUMBER = {7-8},
     PAGES = {355--358},
      ISSN = {1631-073X},
   MRCLASS = {37P15 (11G50 14G05 37P05 37P30)},
  MRNUMBER = {2607018 (2011e:37186)},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.1016/j.crma.2010.02.010},
       URL = {http://dx.doi.org/10.1016/j.crma.2010.02.010},
}
@comment{UPDATE}
@misc {arxiv1102.1432,
    AUTHOR = {Faber, Xander},
    TITLE = {Topology and Geometry of the {B}erkovich Ramification Locus 
           for Rational Functions},
     YEAR = {2011},
     NOTE = {\url{arXiv:1102.1432}},
}
@article {arxiv1104.0943,
    AUTHOR = {Faber, Xander},
     TITLE = {Topology and geometry of the {B}erkovich ramification locus
              for rational functions, {II}},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {356},
      YEAR = {2013},
    NUMBER = {3},
     PAGES = {819--844},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {Preliminary Data},
  MRNUMBER = {3063898},
       DOI = {10.1007/s00208-012-0872-3},
       URL = {http://dx.doi.org/10.1007/s00208-012-0872-3},
}
@comment{UPDATE}
@misc {arxiv1102.1433,
    AUTHOR = {Faber, Xander},
    TITLE = {Rational Functions with a Unique Critical Point},
     YEAR = {2011},
     NOTE = {\url{arXiv:1102.1433}},
}
@article {MR3283655,
    AUTHOR = {Faber, Xander},
     TITLE = {Benedetto's trick and existence of rational preperiodic
              structures for quadratic polynomials},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {143},
      YEAR = {2015},
    NUMBER = {2},
     PAGES = {685--694},
      ISSN = {0002-9939},
   MRCLASS = {37P35 (37P05 37P40)},
  MRNUMBER = {3283655},
MRREVIEWER = {Thomas Ward},
       DOI = {10.1090/S0002-9939-2014-12328-8},
       URL = {http://dx.doi.org/10.1090/S0002-9939-2014-12328-8},
}
@comment{ ----- Blank form for ArXiv papers ---}
@comment{UPDATE}
@misc {arxiv2012.03073,
    AUTHOR = {Faber, Xander and Pardue, Keith and Zelinsky, David},
    TITLE = {Cross-Ratios of Scheme-Valued Points},
     YEAR = {2020},
     NOTE = {\url{arXiv:2012.03073}},
}
@comment{arxiv0903.1344}
@article {MR2863906,
    AUTHOR = {Faber, Xander and Granville, Andrew},
     TITLE = {Prime factors of dynamical sequences},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {661},
      YEAR = {2011},
     PAGES = {189--214},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {37P05 (11B37)},
  MRNUMBER = {2863906 (2012j:37120)},
MRREVIEWER = {Thomas Ward},
       DOI = {10.1515/CRELLE.2011.081},
       URL = {http://dx.doi.org/10.1515/CRELLE.2011.081},
}
@article {arxiv:0810.1715,
    AUTHOR = {Faber, Xander and Hutz, Benjamin and Stoll, Michael},
     TITLE = {On the number of rational iterated preimages of the origin
              under quadratic dynamical systems},
   JOURNAL = {Int. J. Number Theory},
  FJOURNAL = {International Journal of Number Theory},
    VOLUME = {7},
      YEAR = {2011},
    NUMBER = {7},
     PAGES = {1781--1806},
      ISSN = {1793-0421},
   MRCLASS = {37P15 (11G30 11G40 14G05 37P05)},
  MRNUMBER = {2854215 (2012i:37141)},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.1142/S1793042111004162},
       URL = {http://dx.doi.org/10.1142/S1793042111004162},
}

@article {arxiv:0805.0441,
    AUTHOR = {Faber, Xander and Hutz, Benjamin and Ingram, Patrick and
              Jones, Rafe and Manes, Michelle and Tucker, Thomas J. and
              Zieve, Michael E.},
     TITLE = {Uniform bounds on pre-images under quadratic dynamical
              systems},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {16},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {87--101},
      ISSN = {1073-2780},
   MRCLASS = {14G25 (11G18 14G05 37Bxx 37Fxx)},
  MRNUMBER = {MR2480563},
}
@comment{arxiv1905.09378}
@article {MR3996342,
    AUTHOR = {Faber, Xander and Manes, Michelle and Walton, Laura},
     TITLE = {An alternate proof of idempotent relations among periodic
              points and quotients},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {205},
      YEAR = {2019},
     PAGES = {44--49},
      ISSN = {0022-314X},
   MRCLASS = {14G15 (37P05)},
  MRNUMBER = {3996342},
MRREVIEWER = {Jorge Mello},
       DOI = {10.1016/j.jnt.2019.05.001},
       URL = {https://doi.org/10.1016/j.jnt.2019.05.001},
}
@comment{UPDATE}
@misc {arxiv2003.05205,
    AUTHOR = {Faber, Xander and Petsche, Clayton},
    TITLE = {Totally {$T$}-adic functions of small height},
     YEAR = {2020},
     NOTE = {\url{arXiv:2003.05205}},
}
@article {MR3283753,
    AUTHOR = {Faber, Xander and Manes, Michelle and Viray, Bianca},
     TITLE = {Computing conjugating sets and automorphism groups of rational
              functions},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {423},
      YEAR = {2015},
     PAGES = {1161--1190},
      ISSN = {0021-8693},
   MRCLASS = {37P05 (11Y16)},
  MRNUMBER = {3283753},
       DOI = {10.1016/j.jalgebra.2014.08.048},
       URL = {http://dx.doi.org/10.1016/j.jalgebra.2014.08.048},
}
@comment{UPDATE}
@misc {arxiv1212.6409,
    AUTHOR = {Faber, Xander and Towsley, Adam},
    TITLE = {Newton's Method Over Global Height Fields}, 
     YEAR = {2012},
     NOTE = {\url{arXiv:1212.6409}},
}
@article {arxiv1003.1236,
    AUTHOR = {Faber, Xander and Voloch, Jos{\'e} Felipe},
     TITLE = {On the number of places of convergence for {N}ewton's method
              over number fields},
   JOURNAL = {J. Th\'eor. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
    VOLUME = {23},
      YEAR = {2011},
    NUMBER = {2},
     PAGES = {387--401},
      ISSN = {1246-7405},
   MRCLASS = {37P05 (37P20)},
  MRNUMBER = {2817936 (2012f:37180)},
MRREVIEWER = {Joseph H. Silverman},
       URL = {http://jtnb.cedram.org/item?id=JTNB_2011__23_2_387_0},
}
@comment{UPDATE}
@misc {arxiv2010.03474,
    AUTHOR = {Fabiani, Silvia},
    TITLE = {Cycles for rational maps over global function fields with one prime of bad reduction},
     YEAR = {2020},
     NOTE = {\url{arXiv:2010.03474}},
}

@article {MR1707699,
    AUTHOR = {Fagella, N{\'u}ria and Llibre, Jaume},
     TITLE = {Periodic points of holomorphic maps via {L}efschetz numbers},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {352},
      YEAR = {2000},
    NUMBER = {10},
     PAGES = {4711--4730},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {55M20 (37F10)},
  MRNUMBER = {MR1707699 (2001b:55003)},
MRREVIEWER = {Evelyn L. Hart},
}
@article {MR3218803,
    AUTHOR = {Fakhruddin, Najmuddin},
     TITLE = {The algebraic dynamics of generic endomorphisms of
              {$\mathbb{P}^n$}},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {8},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {587--608},
      ISSN = {1937-0652},
   MRCLASS = {37P55 (37F10)},
  MRNUMBER = {3218803},
       DOI = {10.2140/ant.2014.8.587},
       URL = {http://dx.doi.org/10.2140/ant.2014.8.587},
}
@article {MR1995861,
    AUTHOR = {Fakhruddin, Najmuddin},
     TITLE = {Questions on self maps of algebraic varieties},
   JOURNAL = {J. Ramanujan Math. Soc.},
  FJOURNAL = {Journal of the Ramanujan Mathematical Society},
    VOLUME = {18},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {109--122},
      ISSN = {0970-1249},
   MRCLASS = {14G05 (37A45)},
  MRNUMBER = {MR1995861 (2004f:14038)},
MRREVIEWER = {Yuri Tschinkel},
}
@article {MR1836365,
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      YEAR = {2001},
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      ISSN = {0253-4142},
   MRCLASS = {11G35 (11G20 14G20 14G25)},
  MRNUMBER = {MR1836365 (2003a:11075)},
MRREVIEWER = {Atsushi Moriwaki},
}
@incollection {MR861971,
    AUTHOR = {Faltings, Gerd},
     TITLE = {Finiteness theorems for abelian varieties over number fields},
 BOOKTITLE = {Arithmetic geometry \textup{(}Storrs, Conn., 1984\textup{)}},
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 PUBLISHER = {Springer},
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      YEAR = {1986},
   MRCLASS = {11G10 (14K15)},
  MRNUMBER = {MR861971},
}

@article {MR718935,
    AUTHOR = {Faltings, Gerd},
     TITLE = {Endlichkeitss\"atze f\"ur abelsche {V}ariet\"aten \"uber
              {Z}ahlk\"orpern},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {73},
      YEAR = {1983},
    NUMBER = {3},
     PAGES = {349--366},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11D41 (11G30 14G25)},
  MRNUMBER = {MR718935 (85g:11026a)},
MRREVIEWER = {James Milne},
}

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@article {MR3073568,
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}
@article {MR3345863,
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}
@article {MR3622078,
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  MRNUMBER = {3622078},
       URL = {https://doi.org/10.3934/dcds.2017135},
}
@comment{UPDATE}
@misc {arxiv1408.4574,
    AUTHOR = {Fan, Shilei and Liao, Lingmin},
    TITLE = {Dynamics of the square mapping on the ring of $p$-adic integers},
     YEAR = {2014},
     NOTE = {\url{arXiv:1408.4574}},
}
@incollection {MR3782300,
    AUTHOR = {Fan, Shilei and Liao, Lingmin},
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@book {MR1233388,
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@article {fatou:1920,
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     PAGES = {33--94 and 208--314},
}

@article {MR2021001,
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}
@article {MR1759437,
    AUTHOR = {Favre, Charles},
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              {K}ato surfaces. {I}},
   JOURNAL = {J. Math. Pures Appl. (9)},
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     PAGES = {475--514},
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   MRCLASS = {32H50 (32B10 32J05 37F99)},
  MRNUMBER = {1759437},
MRREVIEWER = {Eric Bedford},
       DOI = {10.1016/S0021-7824(00)00162-8},
       URL = {https://doi.org/10.1016/S0021-7824(00)00162-8},
}
@comment{UPDATE}
@misc {arxiv1302.0810,
    AUTHOR = {Favre, Charles and Gauthier, Thomas},
    TITLE = {Distribution of postcritically finite polynomials},
     YEAR = {2013},
     NOTE = {\url{arXiv:1302.0810}},
}
@comment{arxiv1603.05126}
@article {MR3801434,
    AUTHOR = {Favre, Charles and Gauthier, Thomas},
     TITLE = {Classification of Special Curves in the Space of Cubic
              Polynomials},
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  FJOURNAL = {International Mathematics Research Notices. IMRN},
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    NUMBER = {2},
     PAGES = {362----411},
      ISSN = {1073-7928},
   MRCLASS = {37P55 (14H10)},
  MRNUMBER = {3801434},
       DOI = {10.1093/imrn/rnw245},
       URL = {https://doi.org/10.1093/imrn/rnw245},
}
@article {MR3864204,
    AUTHOR = {Favre, Charles and Gauthier, Thomas},
     TITLE = {Continuity of the {G}reen function in meromorphic families of
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   JOURNAL = {Algebra Number Theory},
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  MRNUMBER = {3864204},
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       URL = {https://doi.org/10.2140/ant.2018.12.1471},
}
@comment{UPDATE} @comment{This is a 246 page monograph}
@misc {arxiv2004.13801,
    AUTHOR = {Favre, Charles and Gauthier, Thomas},
    TITLE = {The arithmetic of polynomial dynamical pairs},
     YEAR = {2020},
     NOTE = {\url{arXiv:2004.13801}},
}
@article {MR2339287,
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     TITLE = {Eigenvaluations},
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  FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
              Quatri\`eme S\'erie},
    VOLUME = {40},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {309--349},
      ISSN = {0012-9593},
     CODEN = {ASENAH},
   MRCLASS = {37F10 (32H50)},
  MRNUMBER = {2339287 (2008j:37091)},
MRREVIEWER = {Romain Dujardin},
       DOI = {10.1016/j.ansens.2007.01.002},
       URL = {http://dx.doi.org/10.1016/j.ansens.2007.01.002},
}

@article {arxiv0711.2770,
    AUTHOR = {Favre, Charles and Jonsson, Mattias},
     TITLE = {Dynamical compactifications of {${\mathbf{C}}^2$}},
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      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {32H50 (32J05 32U35 37F10)},
  MRNUMBER = {2753603 (2012d:32025)},
MRREVIEWER = {Araceli Bonifant},
       DOI = {10.4007/annals.2011.173.1.6},
       URL = {http://dx.doi.org/10.4007/annals.2011.173.1.6},
}
@article {MR2925406,
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@article {MR2092012,
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     TITLE = {Th\'eor\`eme d'\'equidistribution de {B}rolin en dynamique
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   JOURNAL = {C.~R.~Math. Acad. Sci. Paris},
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    NUMBER = {4},
     PAGES = {271--276},
      ISSN = {1631-073X},
   MRCLASS = {37F10 (11S85)},
  MRNUMBER = {MR2092012},
}

@article {arxiv0407471,
    AUTHOR = {Favre, Charles and Rivera-Letelier, Juan},
     TITLE = {\'{E}quidistribution quantitative des points de petite hauteur
              sur la droite projective},
   JOURNAL = {Math. Ann.},
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   MRCLASS = {11G50 (37F10)},
  MRNUMBER = {MR2221116},
      NOTE = {Corrigendum: Math. Ann. 339 (2007), 799--801},
}
@article {MR2578470,
    AUTHOR = {Favre, Charles and Rivera-Letelier, Juan},
     TITLE = {Th\'eorie ergodique des fractions rationnelles sur un corps
              ultram\'etrique},
   JOURNAL = {Proc. Lond. Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {100},
      YEAR = {2010},
    NUMBER = {1},
     PAGES = {116--154},
      ISSN = {0024-6115},
   MRCLASS = {37Pxx (11S85)},
  MRNUMBER = {MR2578470},
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}
@article {arxiv1011.2854,
    AUTHOR = {Favre, Charles and Wulcan, Elizabeth},
     TITLE = {Degree growth of monomial maps and {M}c{M}ullen's polytope
              algebra},
   JOURNAL = {Indiana Univ. Math. J.},
  FJOURNAL = {Indiana University Mathematics Journal},
    VOLUME = {61},
      YEAR = {2012},
    NUMBER = {2},
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      ISSN = {0022-2518},
     CODEN = {IUMJAB},
   MRCLASS = {32H50 (52A39)},
  MRNUMBER = {3043585},
       DOI = {10.1512/iumj.2012.61.4555},
       URL = {http://dx.doi.org/10.1512/iumj.2012.61.4555},
}
@misc {arxiv2102.12168,
    AUTHOR = {Fernandes, Gwladys},
    TITLE = {A survey on the hypertranscendence of the solutions of
                  the {S}chr{\"o}der's, {B}{\"o}ttcher's and {A}bel's
                  equations},
     YEAR = {2021},
     NOTE = {\url{arXiv:2102.12168}},
}


@comment{UPDATE}
@misc {arxiv0503720,
    AUTHOR = {Fernandez, Gabriela},
    TITLE = {Wandering {F}atou components on {$p$}-adic polynomial dynamics},
     YEAR = {2004},
     NOTE = {\url{ArXiv:math.DS/0503720}},
}
@comment{Rivera-Letelier notes: Fernandez shows that Benedetto's
examples are dense in an open subset of the space of polynomials over
$C_p$ of a given degree $\ge p + 1$.}

@article {MR3787342,
    AUTHOR = {Ferraguti, Andrea},
     TITLE = {The set of stable primes for polynomial sequences with large
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   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
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      YEAR = {2018},
    NUMBER = {7},
     PAGES = {2773--2784},
      ISSN = {0002-9939},
   MRCLASS = {11R32 (11R45 20E08)},
  MRNUMBER = {3787342},
       DOI = {10.1090/proc/13958},
       URL = {https://doi.org/10.1090/proc/13958},
}
@comment{UPDATE}
@misc {arxiv1805.03097,
    AUTHOR = {Ferraguti, Andrea and Micheli, Giacomo},
    TITLE = {Complete classification of permutation rational functions of degree three over finite fields},
     YEAR = {2018},
     NOTE = {\url{arXiv:1805.03097}},
}
@comment{UPDATE}
@misc {arxiv1905.00506,
    AUTHOR = {Ferraguti, Andrea and Micheli, Giacomo},
    TITLE = {An equivariant isomorphism theorem for mod {$\mathfrak{p}$} reductions of arboreal {G}alois representations},
     YEAR = {2019},
     NOTE = {\url{arXiv:1905.00506}},
}
@comment{arXiv:1604.05223}
@incollection {MR3649090,
    AUTHOR = {Ferraguti, Andrea and Micheli, Giacomo and Schnyder, Reto},
     TITLE = {On sets of irreducible polynomials closed by composition},
 BOOKTITLE = {Arithmetic of finite fields},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {10064},
     PAGES = {77--83},
 PUBLISHER = {Springer, Cham},
      YEAR = {2016},
   MRCLASS = {11T06},
  MRNUMBER = {3649090},
MRREVIEWER = {LongJiang Qu},
}
@comment{UPDATE}
@misc {arxiv1701.06040,
    AUTHOR = {Ferraguti, Andrea and Micheli, Giacomo and Schnyder, Reto},
    TITLE = {Irreducible compositions of degree two polynomials over finite fields have regular structure},
     YEAR = {2017},
     NOTE = {to appear in {\em The Quarterly Journal of Mathematics}. \url{arXiv:1701.06040}},
}
@comment{UPDATE}
@misc {arxiv1907.08608,
    AUTHOR = {Ferraguti, Andrea and Pagano, Carlo and Casazza, Daniele},
    TITLE = {The inverse problem for arboreal {G}alois representations of index two}, 
     YEAR = {2019},
     NOTE = {\url{arXiv:1907.08608}},
}
@comment{UPDATE}
@misc {arxiv2004.02847,
    AUTHOR = {Ferraguti, Andrea and Pagano, Carlo},
    TITLE = {Constraining images of quadratic arboreal representations},
     YEAR = {2020},
     NOTE = {\url{arXiv:2004.02847}},
}
@comment{UPDATE}
@misc {arxiv2203.10034,
    AUTHOR = {Ferraguti, Andrea and Ostafe, Alina and Zannier, Umberto},
    TITLE = {Cyclotomic and abelian points in backward orbits of rational functions},
     YEAR = {2022},
     NOTE = {\url{arXiv:2203.10034}},
}
@comment{UPDATE}
@misc {arxiv1210.7885,
    AUTHOR = {Fili, Paul and Miner, Zachary},
    TITLE = {Equidistribution and the heights of totally real and 
         totally $p$-adic numbers},
     YEAR = {2012},
     NOTE = {\url{arXiv:1210.7885}},
}
@comment{UPDATE}
@misc {arxiv2109.11184,
    AUTHOR = {Paul Fili and Lukas Pottmeyer and Mingming Zhang},
    TITLE = {Wandering points for the {M}ahler measure},
     YEAR = {2021},
     NOTE = {\url{arXiv:2109.11184}},
}
@comment{UPDATE}
@misc {arxiv1911.06288,
    AUTHOR = {Fili, Paul and Pottmeyer, Lukas and Zhang, Mingming},
    TITLE = {On the behavior of {M}ahler's measure under iteration}, 
     YEAR = {2019},
     NOTE = {\url{arXiv:1911.06288}},
}
@article {MR4009394,
    AUTHOR = {Fili, Paul A. and Pottmeyer, Lukas},
     TITLE = {Quantitative height bounds under splitting conditions},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {372},
      YEAR = {2019},
    NUMBER = {7},
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      ISSN = {0002-9947},
   MRCLASS = {11G50 (11R06 31A15 37P30)},
  MRNUMBER = {4009394},
       DOI = {10.1090/tran/7656},
       URL = {https://doi.org/10.1090/tran/7656},
}
@article {MR3959360,
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       URL = {https://doi.org/10.3934/jmd.2019007},
}
@comment{UPDATE}
@misc {arxiv2205.05579,
    AUTHOR = {Finch, Steven},
    TITLE = {Components and Cycles of Random Mappings},
     YEAR = {2022},
     NOTE = {\url{arXiv:2205.05579}},
}  
@incollection {MR1083961,
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    SERIES = {Lecture Notes in Comput. Sci.},
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     PAGES = {329--354},
 PUBLISHER = {Springer, Berlin},
      YEAR = {1990},
   MRCLASS = {05A15 (60C05)},
  MRNUMBER = {1083961},
       DOI = {10.1007/3-540-46885-4_34},
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}
@article {MR519546,
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    NUMBER = {3-4},
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MRREVIEWER = {P. Orlik},
}
COMMENT{This is an excellent review of a large segment of results
  concerning finite groups G acting on an l-dimensional vector space V
  over a field k, and generated by reflections.}

@comment{UPDATE}
@misc {arxiv2105.10055,
    AUTHOR = {Floyd, William and Kim, Daniel and Koch, Sarah and Parry, Walter and Saenz, Edgar},
    TITLE = {Realizing polynomial portraits},
     YEAR = {2021},
     NOTE = {\url{arXiv:2105.10055}},
}


@article {flynnetal:cyclesofquads,
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@comment{arxiv1108.4132}
@article {MR3190008,
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}

@incollection {MR1190986,
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}

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  MRNUMBER = {MR1332961 (96k:32057)},
MRREVIEWER = {Eric Bedford},
}

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@incollection {MR1369137,
    AUTHOR = {Forn{\ae}ss, John Erik and Sibony, Nessim},
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@article {MR1145616,
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@article {MR1779395,
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@article {MR991490,
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@comment{UPDATE}
@misc {arxiv2009.12251,
    AUTHOR = {Fu, Hang},
    TITLE = {Uniform unlikely intersections for unicritical polynomials},
     YEAR = {2020},
     NOTE = {\url{arXiv:2009.12251}},
}
@comment{UPDATE}
@misc {arxiv2201.12588,
    AUTHOR = {Fuchs, Elena and Litman, Matthew and Silverman, Joseph H. and Tran, Austin},
    TITLE = {Orbits on {K3} Surfaces of {M}arkoff Type},
     YEAR = {2022},
     NOTE = {\url{arXiv:2201.12588}},
}
@article {MR2376676,
    AUTHOR = {Fujimura, Masayo},
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      YEAR = {2007},
    NUMBER = {2},
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   MRCLASS = {30E20 (37C25 37F10)},
  MRNUMBER = {2376676},
       DOI = {10.1007/BF03321649},
       URL = {https://doi.org/10.1007/BF03321649},
}

@incollection {MR2509692,
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  MRNUMBER = {2509692 (2010g:14052)},
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@inproceedings {MR1810003,
    AUTHOR = {Fujimura, Masayo and Nishizawa, Kiyoko},
     TITLE = {Moduli spaces and symmetry loci of polynomial maps},
 BOOKTITLE = {Proceedings of the 1997 {I}nternational {S}ymposium on
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}
@incollection {MR2405714,
    AUTHOR = {Fujimura, Masayo and Taniguchi, Masahiko},
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    SERIES = {OCAMI Stud.},
    VOLUME = {2},
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      YEAR = {2007},
   MRCLASS = {37F10 (30C10)},
  MRNUMBER = {2405714},
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@book {MR1644323,
    AUTHOR = {Fulton, William},
     TITLE = {Intersection theory},
    SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A
              Series of Modern Surveys in Mathematics [Results in
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              Surveys in Mathematics]},
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   EDITION = {Second},
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     PAGES = {xiv+470},
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       DOI = {10.1007/978-1-4612-1700-8},
       URL = {http://dx.doi.org/10.1007/978-1-4612-1700-8},
}
@article {MR3262033,
    AUTHOR = {Furno, Joanna},
     TITLE = {Singular {$p$}-adic transformations for {B}ernoulli product
              measures},
   JOURNAL = {New York J. Math.},
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    VOLUME = {20},
      YEAR = {2014},
     PAGES = {799--812},
      ISSN = {1076-9803},
   MRCLASS = {37P05 (37A40)},
  MRNUMBER = {3262033},
       URL = {http://nyjm.albany.edu:8000/j/2014/20_799.html},
}
@article {MR3306157,
    AUTHOR = {Furno, Joanna},
     TITLE = {Approximations for {$p$}-adic transitive isometries},
   JOURNAL = {Topology Proc.},
  FJOURNAL = {Topology Proceedings},
    VOLUME = {46},
      YEAR = {2015},
     PAGES = {323--338},
      ISSN = {0146-4124},
   MRCLASS = {37P05 (11K41 37A40)},
  MRNUMBER = {3306157},
}
@comment{--GGG-- }
@comment{UPDATE}
@misc {arxiv2103.16533,
    AUTHOR = {Garton, Derek},
    TITLE = {Periodic points of polynomials over finite fields},
     YEAR = {2021},
     NOTE = {\url{arXiv:2103.16533}},
}
@comment{UPDATE}
@misc {arxiv2208.13281,
    AUTHOR = {Garton, Derek},
    TITLE = {Periodic points of rational functions of large degree over finite fields},
     YEAR = {2022},
     NOTE = {\url{arXiv:2208.13281}},
}
@article {MR3598828,
    AUTHOR = {Galateau, Aur\'{e}lien and Mah\'{e}, Val\'{e}ry},
     TITLE = {Some consequences of {M}asser's counting theorem on elliptic
              curves},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {285},
      YEAR = {2017},
    NUMBER = {1-2},
     PAGES = {613--629},
      ISSN = {0025-5874},
   MRCLASS = {11G50},
  MRNUMBER = {3598828},
MRREVIEWER = {Robin de Jong},
       DOI = {10.1007/s00209-016-1728-4},
       URL = {https://doi.org/10.1007/s00209-016-1728-4},
}

@article {MR1363145,
    AUTHOR = {Gallas, Jason A. C.},
     TITLE = {Units: remarkable points in dynamical systems},
   JOURNAL = {Phys. A},
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    VOLUME = {222},
      YEAR = {1995},
    NUMBER = {1-4},
     PAGES = {125--151},
      ISSN = {0378-4371},
     CODEN = {PHYSAG},
   MRCLASS = {58F20 (11R27 58F08)},
  MRNUMBER = {MR1363145 (96m:58205)},
MRREVIEWER = {J. C. Lagarias},
}
@article {MR4071895,
    AUTHOR = {Gallas, Jason A. C.},
     TITLE = {Field discriminants of cyclotomic period equations},
   JOURNAL = {Internat. J. Modern Phys. C},
  FJOURNAL = {International Journal of Modern Physics C. Computational
              Physics and Physical Computation},
    VOLUME = {31},
      YEAR = {2020},
    NUMBER = {2},
     PAGES = {2050021, 20},
      ISSN = {0129-1831},
   MRCLASS = {11R18 (11R29 37P05)},
  MRNUMBER = {4071895},
       DOI = {10.1142/S0129183120500217},
       URL = {https://doi.org/10.1142/S0129183120500217},
}
@article {MR4024562,
    AUTHOR = {Gamburd, Alexander and Magee, Michael and Ronan, Ryan},
     TITLE = {An asymptotic formula for integer points on
              {M}arkoff-{H}urwitz varieties},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {190},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {751--809},
      ISSN = {0003-486X},
   MRCLASS = {11D45 (11D25 11D41 11J70 37D25 37D35)},
  MRNUMBER = {4024562},
MRREVIEWER = {Paul M. Voutier},
       DOI = {10.4007/annals.2019.190.3.2},
       URL = {https://doi.org/10.4007/annals.2019.190.3.2},
}
@article {MR3962573,
    AUTHOR = {Gangavarapu, Venkata Krishna Kishore},
     TITLE = {Torsion elements of the {N}ottingham group of order {$p^2$}
              and type {$\langle2,m\rangle$}},
   JOURNAL = {J. Ramanujan Math. Soc.},
  FJOURNAL = {Journal of the Ramanujan Mathematical Society},
    VOLUME = {34},
      YEAR = {2019},
    NUMBER = {2},
     PAGES = {231--243},
      ISSN = {0970-1249},
   MRCLASS = {11S31 (20D15 20E18 37P35)},
  MRNUMBER = {3962573},
}
@comment{UPDATE}
@misc {arxiv2105.15085,
    AUTHOR = {Gao, Yan and Ge, Tangli and K{\"u}hne, Lars},
    TITLE = {The Uniform {M}ordell--{L}ang Conjecture},
     YEAR = {2021},
     NOTE = {\url{arXiv:2105.15085}},
}
@comment{UPDATE}
@misc {arxiv2104.03431,
    AUTHOR = {Gao, Yan},
    TITLE = {Recent developments of the Uniform {M}ordell--{L}ang Conjecture},
     YEAR = {2021},
     NOTE = {\url{arXiv:2104.03431}},
}
@comment{The author studies the units in the moduli space of Henon maps}
@article {MR3460633,
    AUTHOR = {Gao, Yan},
     TITLE = {Preperiodic dynatomic curves for {$z\mapsto z^d+c$}},
   JOURNAL = {Fund. Math.},
  FJOURNAL = {Fundamenta Mathematicae},
    VOLUME = {233},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {37--69},
      ISSN = {0016-2736},
   MRCLASS = {37F45 (12F10 14H50 37F10 37P05)},
  MRNUMBER = {3460633},
MRREVIEWER = {Kevin M. Pilgrim},
       DOI = {10.4064/fm91-12-2015},
       URL = {https://doi.org/10.4064/fm91-12-2015},
}
@article {MR3202010,
    AUTHOR = {Gao, Yan and Ou, YaFei},
     TITLE = {The dynatomic periodic curves for polynomial
                  {$z\mapsto{z}^d+c$} are smooth and irreducible},
   JOURNAL = {Sci. China Math.},
  FJOURNAL = {Science China. Mathematics},
    VOLUME = {57},
      YEAR = {2014},
    NUMBER = {6},
     PAGES = {1175--1192},
      ISSN = {1674-7283},
   MRCLASS = {37F45 (14H30 14H45)},
  MRNUMBER = {3202010},
       DOI = {10.1007/s11425-014-4807-1},
       URL = {https://doi.org/10.1007/s11425-014-4807-1},
}
@comment{arxiv1209.4396}
@article {MR3130359,
    AUTHOR = {Gassert, T. Alden},
     TITLE = {Chebyshev action on finite fields},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {315},
      YEAR = {2014},
     PAGES = {83--94},
      ISSN = {0012-365X},
   MRCLASS = {05C31},
  MRNUMBER = {3130359},
       DOI = {10.1016/j.disc.2013.10.014},
       URL = {http://dx.doi.org/10.1016/j.disc.2013.10.014},
}
@article {arxiv1004.5511,
    AUTHOR = {Gasull, Armengol and Ma{\~n}osa, V{\'{\i}}ctor and Xarles,
              Xavier},
     TITLE = {Rational periodic sequences for the {L}yness recurrence},
   JOURNAL = {Discrete Contin. Dyn. Syst.},
  FJOURNAL = {Discrete and Continuous Dynamical Systems. Series A},
    VOLUME = {32},
      YEAR = {2012},
    NUMBER = {2},
     PAGES = {587--604},
      ISSN = {1078-0947},
   MRCLASS = {39A20 (11G05 37P15 39A23)},
  MRNUMBER = {2837074 (2012i:39008)},
MRREVIEWER = {Hassan Sedaghat},
       DOI = {10.3934/dcds.2012.32.587},
       URL = {http://dx.doi.org/10.3934/dcds.2012.32.587},
}
@comment{UPDATE}
@misc {arxiv1712.01407,
    AUTHOR = {Gathen, Joachim von zur},
    TITLE = {Iteration entropy},
     YEAR = {2017},
     NOTE = {\url{arXiv:1712.01407}},
}
@comment{UPDATE}
@misc {arxiv2105.02479,
    AUTHOR = {Gauthier, Thomas},
    TITLE = {Good height functions on quasi-projective varieties: equidistribution and applications in dynamics},
     YEAR = {2021},
     NOTE = {\url{arXiv:2105.02479}},
}
@comment{UPDATE}
@misc {arxiv1912.07907,
    AUTHOR = {Gauthier, Thomas and  Vigny, Gabriel},
    TITLE = {The Geometric Dynamical {N}orthcott and {B}ogomolov Properties},
     YEAR = {2019},
     NOTE = {\url{arXiv:1912.07907}},
}
@comment{UPDATE}
@misc {arxiv2010.16291,
    AUTHOR = {Gauthier, Thomas and  Vigny, Gabriel},
    TITLE = {The Geometric Dynamical {N}orthcott Property For Regular Polynomial Automorphisms of the Affine Plane},
     YEAR = {2020},
     NOTE = {\url{arXiv:2010.16291}},
}

@comment{UPDATE}
@misc {arxiv1803.06859,
    AUTHOR = {Gauthier, Thomas and Okuyama, Yusuke and Vigny, Gabriel},
    TITLE = {Approximation of non-archimedean {L}yapunov exponents and applications over global fields},
     YEAR = {2018},
     NOTE = {\url{arXiv:1803.06859}},
}

@book {MR785216,
       KEY = {Geometry of K3 surfaces},
     TITLE = {G\'eom\'etrie des surfaces {$K3$}: modules et p\'eriodes},
      NOTE = {Papers from the seminar held in Palaiseau, October
              1981--January 1982,
              Ast\'erisque No. 126 (1985)},
 PUBLISHER = {Soci\'et\'e Math\'ematique de France},
   ADDRESS = {Paris},
      YEAR = {1985},
     PAGES = {1--193},
      ISSN = {0303-1179},
   MRCLASS = {32J15 (14J25 14J28 53C25)},
  MRNUMBER = {MR785216 (87h:32052)},
MRREVIEWER = {Werner Kleinert},
}

@comment{UPDATE}
@misc {arxiv2105.15090,
    AUTHOR = {Ge, Tangli},
    TITLE = {Uniformity of quadratic points},
     YEAR = {2021},
     NOTE = {\url{arXiv:2105.15090}},
}

@phdthesis{getachew:thesis, 
   AUTHOR = {Getachew, Selemon},
    TITLE = {Galois Theory of Polynomial Iterates},
   SCHOOL = {Brown University},
     YEAR = {2000}
	}
@article {MR2255176,
    AUTHOR = {Ghioca, Dragos},
     TITLE = {Equidistribution for torsion points of a {D}rinfeld module},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {336},
      YEAR = {2006},
    NUMBER = {4},
     PAGES = {841--865},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {11G09 (11G50)},
  MRNUMBER = {MR2255176},
}
@comment{UPDATE}
@misc {arxiv1307.3747,
    AUTHOR = {Ghioca, Dragos},
    TITLE = {Integral points for {D}rinfeld modules},
     YEAR = {2013},
     NOTE = {\url{arXiv:1307.3747}},
}
@article {MR3235993,
    AUTHOR = {Ghioca, Dragos},
     TITLE = {The dynamical {M}ordell-{L}ang conjecture},
   JOURNAL = {CMS Notes},
  FJOURNAL = {CMS Notes},
    VOLUME = {46},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {14--15},
      ISSN = {1193-9273},
   MRCLASS = {37P55 (11D45 37F10 37P20)},
  MRNUMBER = {3235993},
}
@comment{arxiv1610.00367}
@article {MR3885174,
    AUTHOR = {Ghioca, Dragos},
     TITLE = {The dynamical {M}ordell-{L}ang conjecture in positive
              characteristic},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {371},
      YEAR = {2019},
    NUMBER = {2},
     PAGES = {1151--1167},
      ISSN = {0002-9947},
   MRCLASS = {37P55 (11G10 14G17)},
  MRNUMBER = {3885174},
       DOI = {10.1090/tran/7261},
       URL = {https://doi.org/10.1090/tran/7261},
}
@comment{arxiv1803.03928}
@article {MR3829742,
    AUTHOR = {Ghioca, Dragos and Hu, Fei},
     TITLE = {Density of orbits of endomorphisms of commutative linear
              algebraic groups},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {24},
      YEAR = {2018},
     PAGES = {375--388},
      ISSN = {1076-9803},
   MRCLASS = {37P15 (20G15 32H50)},
  MRNUMBER = {3829742},
}
@comment{arxiv1210.7715}
@article {MR3095224,
    AUTHOR = {Ghioca, Dragos and Hsia, Liang-Chung and Tucker, Thomas J.},
     TITLE = {Preperiodic points for families of polynomials},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {7},
      YEAR = {2013},
    NUMBER = {3},
     PAGES = {701--732},
      ISSN = {1937-0652},
   MRCLASS = {37P05 (37P10)},
  MRNUMBER = {3095224},
       DOI = {10.2140/ant.2013.7.701},
       URL = {http://dx.doi.org/10.2140/ant.2013.7.701},
}
@comment{UPDATE}
@misc {arxiv1804.10561,
    AUTHOR = {Ghioca, D. and Hu, F. and Scanlon, T. and Zannier, U.},
    TITLE = {A variant of the {M}ordell--{L}ang conjecture},
     YEAR = {2018},
     NOTE = {\url{arXiv:1804.10561}},
}
@comment{Proof that gcd(D_{nP},D_{mQ}) is bounded for independent points on elliptic curves over function fields}
@article {MR3778323,
    AUTHOR = {Ghioca, Dragos and Hsia, Liang-Chung and Tucker, Thomas},
     TITLE = {A variant of a theorem by {A}ilon-{R}udnick for elliptic
              curves},
   JOURNAL = {Pacific J. Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {295},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {1--15},
      ISSN = {0030-8730},
   MRCLASS = {11G50 (11G05 11G35 14G25 14H52)},
  MRNUMBER = {3778323},
MRREVIEWER = {J\"{o}rg Jahnel},
       DOI = {10.2140/pjm.2018.295.1},
       URL = {https://doi.org/10.2140/pjm.2018.295.1},
}
@comment{UPDATE}
@misc {arxiv1507.04993,
    AUTHOR = {Ghioca, Dragos and Hsia, Liang-Chung and Tucker, Thomas J.},
    TITLE = {Unlikely Intersection For Two-Parameter Families of Polynomials},
     YEAR = {2015},
     NOTE = {\url{arXiv:1507.04993}},
}

@comment{UPDATE}
@misc {arxiv2108.06732,
    AUTHOR = {Ghioca, D. and Saleh, Sina},
    TITLE = {Zariski dense orbits for regular self-maps of split semiabelian varieties in positive characteristic},
     YEAR = {2021},
     NOTE = {\url{arXiv:2108.06732}},
}

@article {arxiv1505.01447,
    AUTHOR = {Ghioca, D. and Krieger, H. and Nguyen, K. D. and Ye, H.},
     TITLE = {The dynamical {A}ndr\'{e}-{O}ort conjecture: unicritical
              polynomials},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {166},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {1--25},
      ISSN = {0012-7094},
   MRCLASS = {37P45 (37F05 37F45 37F50)},
  MRNUMBER = {3592687},
MRREVIEWER = {Thomas Gauthier},
       DOI = {10.1215/00127094-3673996},
       URL = {https://doi.org/10.1215/00127094-3673996},
}
@article {arxiv1404.6011,
    AUTHOR = {Ghioca, Dragos and Krieger, Holly and Nguyen, Khoa},
     TITLE = {A case of the dynamical {A}ndr\'{e}-{O}ort conjecture},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2016},
    NUMBER = {3},
     PAGES = {738--758},
      ISSN = {1073-7928},
   MRCLASS = {37P55 (14H45 37F05 37F50 37P45)},
  MRNUMBER = {3493432},
MRREVIEWER = {Rafe Jones},
       DOI = {10.1093/imrn/rnv143},
       URL = {https://doi.org/10.1093/imrn/rnv143},
}
@comment{arxiv1604.02529}
@article {MR3747167,
    AUTHOR = {Ghioca, Dragos and Nguyen, Khoa Dang},
     TITLE = {The orbit intersection problem for linear spaces and
              semiabelian varieties},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {24},
      YEAR = {2017},
    NUMBER = {5},
     PAGES = {1263--1283},
      ISSN = {1073-2780},
   MRCLASS = {37P55 (11B37 11D61 14L10)},
  MRNUMBER = {3747167},
MRREVIEWER = {Christian Lehn},
       DOI = {10.4310/MRL.2017.v24.n5.a2},
       URL = {https://doi.org/10.4310/MRL.2017.v24.n5.a2},
}
@comment{arxiv1511.06081}
@article {MR3941498,
    AUTHOR = {Ghioca, Dragos and Nguyen, Khoa and Ye, Hexi},
     TITLE = {The {D}ynamical {M}anin--{M}umford {C}onjecture and the
              {D}ynamical {B}ogomolov {C}onjecture for split rational maps},
   JOURNAL = {J. Eur. Math. Soc. (JEMS)},
  FJOURNAL = {Journal of the European Mathematical Society (JEMS)},
    VOLUME = {21},
      YEAR = {2019},
    NUMBER = {5},
     PAGES = {1571--1594},
      ISSN = {1435-9855},
   MRCLASS = {37P05 (37P30)},
  MRNUMBER = {3941498},
       DOI = {10.4171/JEMS/869},
       URL = {https://doi.org/10.4171/JEMS/869},
}
@comment{arxiv:1705}
@article {MR3826461,
    AUTHOR = {Ghioca, Dragos and Nguyen, Khoa D. and Ye, Hexi},
     TITLE = {The dynamical {M}anin-{M}umford conjecture and the dynamical
              {B}ogomolov conjecture for endomorphisms of {$(\mathbb{P}^1)^n$}},
   JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {154},
      YEAR = {2018},
    NUMBER = {7},
     PAGES = {1441--1472},
      ISSN = {0010-437X},
   MRCLASS = {37P05 (37P30)},
  MRNUMBER = {3826461},
       DOI = {10.1112/s0010437x18007157},
       URL = {https://doi.org/10.1112/s0010437x18007157},
}
@article {MR3784268,
    AUTHOR = {Ghioca, Dragos and Nguyen, Khoa D. and Tucker, Thomas J.},
     TITLE = {Squarefree doubly primitive divisors in dynamical sequences},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
              Society},
    VOLUME = {164},
      YEAR = {2018},
    NUMBER = {3},
     PAGES = {551--572},
      ISSN = {0305-0041},
   MRCLASS = {11B37 (37P35)},
  MRNUMBER = {3784268},
       DOI = {10.1017/S0305004117000500},
       URL = {https://doi.org/10.1017/S0305004117000500},
}
@comment{arxiv1603.05303:orignal title-The dynamical Andre-Ort conj for cubic polys}
@article {MR3801489,
    AUTHOR = {Ghioca, Dragos and Ye, Hexi},
     TITLE = {A {D}ynamical {V}ariant of the {A}ndr\'e-{O}ort {C}onjecture},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2018},
    NUMBER = {8},
     PAGES = {2447--2480},
      ISSN = {1073-7928},
   MRCLASS = {37P35 (14H10)},
  MRNUMBER = {3801489},
       DOI = {10.1093/imrn/rnw314},
       URL = {https://doi.org/10.1093/imrn/rnw314},
}
@comment{UPDATE}
@misc {arxiv1408.5455,
    AUTHOR = {Ghioca, Dragos and Nguyen, Khoa},
    TITLE = {Dynamical Anomalous Subvarieties: Structure and Bounded
                  Height Theorems},
     YEAR = {2014},
     NOTE = {\url{arXiv:1408.5455}},
}
@article {MR3632102,
    AUTHOR = {Ghioca, Dragos and Nguyen, Khoa D.},
     TITLE = {Dynamics of split polynomial maps: uniform bounds for periods
              and applications},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {213--231},
      ISSN = {1073-7928},
   MRCLASS = {37P55 (14R10)},
  MRNUMBER = {3632102},
MRREVIEWER = {Benjamin A. Hutz},
}
@comment{arxiv1407.1573}
@article {MR3349337,
    AUTHOR = {Ghioca, Dragos and Nguyen, Khoa and Tucker, Thomas J.},
     TITLE = {Portraits of preperiodic points for rational maps},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
              Society},
    VOLUME = {159},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {165--186},
      ISSN = {0305-0041},
   MRCLASS = {11G50 (37P30)},
  MRNUMBER = {3349337},
MRREVIEWER = {Thomas Ward},
       DOI = {10.1017/S0305004115000274},
       URL = {http://dx.doi.org/10.1017/S0305004115000274},
}
@comment{UPDATE}
@misc {arxiv1309.5682,
    AUTHOR = {Ghioca, Dragos and Mavraki,  Niki Myrto},
    TITLE = {Variation of the canonical height in a family of rational maps},
     YEAR = {2013},
     NOTE = {\url{arXiv:1309.5682}},
}
@comment{arxiv1412.2029}
@article {MR3557780,
    AUTHOR = {Ghioca, Dragos and Scanlon, Thomas},
     TITLE = {Density of orbits of endomorphisms of abelian varieties},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {369},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {447--466},
      ISSN = {0002-9947},
   MRCLASS = {37P55 (11G10 14G25 14K15 20M14)},
  MRNUMBER = {3557780},
MRREVIEWER = {Alina Ostafe},
       DOI = {10.1090/tran6648},
       URL = {https://doi.org/10.1090/tran6648},
}
@article {arXiv:0704.1333,
    AUTHOR = {Ghioca, D. and Tucker, T. J.},
     TITLE = {A dynamical version of the {M}ordell-{L}ang conjecture for the
              additive group},
   JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {144},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {304--316},
      ISSN = {0010-437X},
   MRCLASS = {11G09 (14K12 37F10)},
  MRNUMBER = {MR2406114 (2009c:11086)},
MRREVIEWER = {Liang-Chung Hsia},
}

@article {arxivNT0609120,
    AUTHOR = {Ghioca, D. and Tucker, T. J.},
     TITLE = {Equidistribution and integral points for {D}rinfeld modules},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {360},
      YEAR = {2008},
    NUMBER = {9},
     PAGES = {4863--4887},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {11G50 (11G09 11J93)},
  MRNUMBER = {MR2403707 (2009c:11095)},
MRREVIEWER = {Lenny Fukshansky},
}
@article {MR2854724,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas J. and Zhang, Shouwu},
     TITLE = {Towards a dynamical {M}anin-{M}umford conjecture},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2011},
    NUMBER = {22},
     PAGES = {5109--5122},
      ISSN = {1073-7928},
   MRCLASS = {37P15 (11G10 37P55)},
  MRNUMBER = {2854724},
MRREVIEWER = {Joseph H. Silverman},
       URL = {https://doi.org/10.1093/imrn/rnq283},
}
@comment{UPDATE}
@misc {arXiv1206.7047,
    AUTHOR = {Ghioca, Dragos and Hsia, Liang-Chung}, 
    TITLE = {Torsion points in families of Drinfeld modules},
     YEAR = {2012},
     NOTE = {\url{arXiv:1206.7047}},
}
                  
@comment{UPDATE}
@misc {arXiv:0705.4047,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas},
    TITLE = {$p$-adic logarithms for polynomial dynamics},
     YEAR = {2007},
     NOTE = {\url{arXiv:0705.4047}},
}
@comment{UPDATE}
@misc {arxiv0710.1669,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas},
    TITLE = {Mordell--{L}ang and {S}kolem--{M}ahler--{L}ech theorems 
               for endomorphisms of semiabelian varieties},
     YEAR = {2007},
     NOTE = {\url{arXiv:0710.1669}},
}

@comment{MR2521481}
@article {arxiv0805.1560,
    AUTHOR = {Ghioca, D. and Tucker, T. J.},
     TITLE = {Periodic points, linearizing maps, and the dynamical
              {M}ordell-{L}ang problem},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {129},
      YEAR = {2009},
    NUMBER = {6},
     PAGES = {1392--1403},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {37P35 (14K12 37P20)},
  MRNUMBER = {2521481 (2010i:37219)},
MRREVIEWER = {Patrick Ingram},
       DOI = {10.1016/j.jnt.2008.09.014},
       URL = {http://dx.doi.org/10.1016/j.jnt.2008.09.014},
}
@article {arxiv:0808.3263,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas J.},
     TITLE = {Proof of a dynamical {B}ogomolov conjecture for lines under
              polynomial actions},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {138},
      YEAR = {2010},
    NUMBER = {3},
     PAGES = {937--942},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {37P05 (11G35 14G40 37P30)},
  MRNUMBER = {2566560 (2011b:37189)},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.1090/S0002-9939-09-10182-X},
       URL = {http://dx.doi.org/10.1090/S0002-9939-09-10182-X},
}
@article {MR3335283,
    AUTHOR = {Ghioca, D. and Hsia, L.-C. and Tucker, T. J.},
     TITLE = {Preperiodic points for families of rational maps},
   JOURNAL = {Proc. Lond. Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {110},
      YEAR = {2015},
    NUMBER = {2},
     PAGES = {395--427},
      ISSN = {0024-6115},
   MRCLASS = {37P30 (11G50)},
  MRNUMBER = {3335283},
       DOI = {10.1112/plms/pdu051},
       URL = {http://dx.doi.org/10.1112/plms/pdu051},
}
@comment{UPDATE}
@misc {arxiv:1102.2769,
    AUTHOR = {Ghioca, Dragos and Hsia, Liang-Chung and Tucker, Thomas},
    TITLE = {Preperiodic points for families of polynomials},
     YEAR = {2011},
     NOTE = {\url{arXiv:1102.2769}},
}
@comment{UPDATE}
@misc {arxiv:1708.06221,
    AUTHOR = {Ghioca, Dragos and Satriano, Matthew},
    TITLE = {Density of orbits of dominant regular self-maps of semiabelian varieties},
     YEAR = {2017},
     NOTE = {Trans. AMS, to appear, \url{arXiv:1708.06221}},
}
@article {arxiv0705.1954,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas J. and Zieve, Michael E.},
     TITLE = {Intersections of polynomials orbits, and a dynamical
              {M}ordell-{L}ang conjecture},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {171},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {463--483},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {37F10 (11C08 14G99)},
  MRNUMBER = {MR2367026 (2008k:37099)},
MRREVIEWER = {Joseph H. Silverman},
}
@article {MR2861079,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas and Zieve, Michael E.},
     TITLE = {The {M}ordell-{L}ang question for endomorphisms of semiabelian
              varieties},
   JOURNAL = {J. Th\'eor. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
    VOLUME = {23},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {645--666},
      ISSN = {1246-7405},
   MRCLASS = {37P55 (11G25 14L10)},
  MRNUMBER = {2861079},
MRREVIEWER = {Kevin Doerksen},
       DOI = {10.5802/jtnb.781},
       URL = {http://dx.doi.org/10.5802/jtnb.781},
}
@article {arxiv0807.3576,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas J. and Zieve, Michael E.},
     TITLE = {Linear relations between polynomial orbits},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {161},
      YEAR = {2012},
    NUMBER = {7},
     PAGES = {1379--1410},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {37P05 (11C08)},
  MRNUMBER = {2922378},
MRREVIEWER = {Kevin Doerksen},
       DOI = {10.1215/00127094-1598098},
       URL = {http://dx.doi.org/10.1215/00127094-1598098},
}
@article {MR3834665,
    AUTHOR = {Ghioca, Dragos and Xie, Junyi},
     TITLE = {Algebraic dynamics of skew-linear self-maps},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {146},
      YEAR = {2018},
    NUMBER = {10},
     PAGES = {4369--4387},
      ISSN = {0002-9939},
   MRCLASS = {37P15 (14E05 37P05)},
  MRNUMBER = {3834665},
       DOI = {10.1090/proc/14104},
       URL = {https://doi.org/10.1090/proc/14104},
}
@comment{arxiv1803.03871}
@article {MR4176829,
    AUTHOR = {Ghioca, Dragos and Xie, Junyi},
     TITLE = {The dynamical {M}ordell-{L}ang conjecture for skew-linear
              self-maps. {A}ppendix by {M}ichael {W}ibmer},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2020},
    NUMBER = {21},
     PAGES = {7433--7453},
      ISSN = {1073-7928},
   MRCLASS = {37P05 (11S82 14E05 39A10)},
  MRNUMBER = {4176829},
       DOI = {10.1093/imrn/rny211},
       URL = {https://doi.org/10.1093/imrn/rny211},
}
@comment{UPDATE}
@misc {ghiocazievelattes2010,
    AUTHOR = {Ghioca, Dragos and Zieve, Michael},
    TITLE = {Latt{\`e}s maps in arbitrary characteristic},
     YEAR = {2008},
     NOTE = {in preparation},
}

@comment{UPDATE}
@misc {arxiv2012.13711,
    AUTHOR = {Ghioca, Dragos and Ostafe, Alina and Saleh, Sina and Shparlinski, Igor E.},
    TITLE = {A sparsity result for the dynamical {M}ordell--{L}ang Conjecture in positive characteristic},
     YEAR = {2020},
     NOTE = {\url{arXiv:2012.13711}},
}

@comment{arxiv1706.06712}
@article {MR4448994,
    AUTHOR = {Ghosh, Amit and Sarnak, Peter},
     TITLE = {Integral points on {M}arkoff type cubic surfaces},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {229},
      YEAR = {2022},
    NUMBER = {2},
     PAGES = {689--749},
      ISSN = {0020-9910},
   MRCLASS = {11D25 (11D45 11J06)},
  MRNUMBER = {4448994},
       DOI = {10.1007/s00222-022-01114-z},
       URL = {https://doi.org/10.1007/s00222-022-01114-z},
}

@comment{UPDATE}
@misc {arxiv2110.11030,
    AUTHOR = {Ghosh, Amit and Meiri, Chen and Sarnak, Peter},
    TITLE = {Commutators in {$\operatorname{SL}_2$} and {M}arkoff surfaces {I}},
     YEAR = {2021},
     NOTE = {\url{arXiv:2110.11030}},
}
@article {MR3263927,
    AUTHOR = {Gignac, William and Ruggiero, Matteo},
     TITLE = {Growth of attraction rates for iterates of a superattracting
              germ in dimension two},
   JOURNAL = {Indiana Univ. Math. J.},
  FJOURNAL = {Indiana University Mathematics Journal},
    VOLUME = {63},
      YEAR = {2014},
    NUMBER = {4},
     PAGES = {1195--1234},
      ISSN = {0022-2518},
   MRCLASS = {32H50 (37F45)},
  MRNUMBER = {3263927},
MRREVIEWER = {Liz Raquel Vivas},
       DOI = {10.1512/iumj.2014.63.5286},
       URL = {https://doi.org/10.1512/iumj.2014.63.5286},
}
@comment{Chapter 5 discusses Brauer-Severi varieties}
@book {MR2266528,
    AUTHOR = {Gille, Philippe and Szamuely, Tam\'as},
     TITLE = {Central simple algebras and {G}alois cohomology},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {101},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2006},
     PAGES = {xii+343},
      ISBN = {978-0-521-86103-8; 0-521-86103-9},
   MRCLASS = {16K20 (14F22 19C30)},
  MRNUMBER = {2266528},
MRREVIEWER = {Gr\'egory Berhuy},
       URL = {https://doi.org/10.1017/CBO9780511607219},
}
@article {MR2153617,
    AUTHOR = {Gil, Juan B. and Robins, Sinai},
     TITLE = {Hecke operators on rational functions. {I}},
   JOURNAL = {Forum Math.},
  FJOURNAL = {Forum Mathematicum},
    VOLUME = {17},
      YEAR = {2005},
    NUMBER = {4},
     PAGES = {519--554},
      ISSN = {0933-7741},
     CODEN = {FOMAEF},
   MRCLASS = {11B37 (05A99)},
  MRNUMBER = {2153617 (2006g:11026)},
MRREVIEWER = {Paul C. Pasles},
       DOI = {10.1515/form.2005.17.4.519},
       URL = {http://dx.doi.org/10.1515/form.2005.17.4.519},
}
@comment{UPDATE}
@misc {arxiv1111.1287,
    AUTHOR = {Giordano Bruno, Anna and Virili, Simone},
    TITLE = {Algebraic {Y}uzvinski Formula},
     YEAR = {2011},
     NOTE = {\url{arXiv:1111.1287}},
}
@comment{algebraic entropy on locally compact abelian groups}

@comment{UPDATE}
@misc {arxiv1006.2500,
    AUTHOR = {Glebsky, Lev},
    TITLE = {Cycles in Repeated Exponentiation Modulo $p^n$},
     YEAR = {2010},
     NOTE = {\url{arXiv:1006.2500}},
}
@article {arxiv0908.3920,
    AUTHOR = {Glebsky, Lev and Shparlinski, Igor E.},
     TITLE = {Short cycles in repeated exponentiation modulo a prime},
   JOURNAL = {Des. Codes Cryptogr.},
  FJOURNAL = {Designs, Codes and Cryptography. An International Journal},
    VOLUME = {56},
      YEAR = {2010},
    NUMBER = {1},
     PAGES = {35--42},
      ISSN = {0925-1022},
   MRCLASS = {11A07 (11T71 37P25)},
  MRNUMBER = {2644246 (2011j:11005)},
MRREVIEWER = {Renate Scheidler},
       DOI = {10.1007/s10623-009-9339-2},
       URL = {http://dx.doi.org/10.1007/s10623-009-9339-2},
}
@incollection {arxivFA0602081,
    AUTHOR = {Gl{\"o}ckner, Helge},
     TITLE = {Aspects of {$p$}-adic non-linear functional analysis},
 BOOKTITLE = {$p$-adic mathematical physics},
    SERIES = {AIP Conf. Proc.},
    VOLUME = {826},
     PAGES = {237--253},
 PUBLISHER = {Amer. Inst. Phys.},
   ADDRESS = {Melville, NY},
      YEAR = {2006},
   MRCLASS = {46S10 (47S10)},
  MRNUMBER = {MR2258689},
}
@comment{arxiv1809.09461}
@article {MR3998214,
    AUTHOR = {Goksel, Vefa},
     TITLE = {Markov processes and some {PCF} quadratic polynomials},
   JOURNAL = {Res. Number Theory},
  FJOURNAL = {Research in Number Theory},
    VOLUME = {5},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {Paper No. 29, 50},
      ISSN = {2522-0160},
   MRCLASS = {11R32 (12E05 20E08 37P15)},
  MRNUMBER = {3998214},
MRREVIEWER = {Nigel Byott},
       DOI = {10.1007/s40993-019-0165-y},
       URL = {https://doi.org/10.1007/s40993-019-0165-y},
}

@comment{UPDATE}
@misc {arxiv1710.06821,
    AUTHOR = {Goksel, Vefa},
    TITLE = {Quadratic Polynomials Whose Large Iterates Are Reducible Modulo Primes},
     YEAR = {2017},
     NOTE = {\url{arXiv:1710.06821}},
}
@misc {arxiv2203.15179,
    AUTHOR = {Goksel, Vefa},
    TITLE = {A note on the factorization of iterated quadratics over finite fields},
     YEAR = {2022},
     NOTE = {\url{arXiv:2203.15179}},
}


@comment{arxiv1806.01208}
@article {MR4074390,
    AUTHOR = {Goksel, Vefa},
     TITLE = {On the orbit of a post-critically finite polynomial of the
              form {$x^d+c$}},
   JOURNAL = {Funct. Approx. Comment. Math.},
  FJOURNAL = {Uniwersytet im. Adama Mickiewicza w Poznaniu. Wydzia\l 
              Matematyki i Informatyki. Functiones et Approximatio
              Commentarii Mathematici},
    VOLUME = {62},
      YEAR = {2020},
    NUMBER = {1},
     PAGES = {95--104},
      ISSN = {0208-6573},
   MRCLASS = {37P15 (11R09)},
  MRNUMBER = {4074390},
       DOI = {10.7169/facm/1799},
       URL = {https://doi.org/10.7169/facm/1799},
}
@comment{UPDATE}
@misc {arxiv1908.07361,
    AUTHOR = {Goksel, Vefa},
    TITLE = {A note on {M}isiurewicz polynomials},
     YEAR = {2019},
     NOTE = {\url{arXiv:1908.07361}},
}
@article {MR4039963,
    AUTHOR = {Goksel, Vefa},
     TITLE = {Irreducibility of iterates of post-critically finite quadratic
              polynomials over {$\mathbb{Q}$}},
   JOURNAL = {Rocky Mountain J. Math.},
  FJOURNAL = {The Rocky Mountain Journal of Mathematics},
    VOLUME = {49},
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@comment{\url{ArXiv:math.FA/0602081}}
@article {MR2727344,
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@comment{arXiv:1206.4979}
@article {MR3231208,
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@book {MR1397498,
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@comment{arxiv1208.2989}
@article {MR3138487,
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@comment{UPDATE}
@misc {arxiv1708.06953,
    AUTHOR = {Granville, Andrew},
    TITLE = {Using Dynamical Systems to Construct Infinitely Many Primes},
     YEAR = {2017},
     NOTE = {\url{arXiv:1708.06953}},
}
@comment{UPDATE}
@misc {arxiv2206.11823,
    AUTHOR = {Granville, Andrew},
    TITLE = {Classifying linear division sequences},
     YEAR = {2022},
     NOTE = {\url{arXiv:2206.11823}},
}
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@article {MR3874674,
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@article {MR4037778,
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@incollection {MR1838286,
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  MRNUMBER = {MR1838286 (2002d:37014)},
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@article {MR1876486,
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@comment{UPDATE}
@misc {arxiv1607.08272,
    AUTHOR = {Gunther, Joseph and Hindes, Wade},
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     NOTE = {\url{arXiv:1607.08272}},
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@comment{--HHH-- }

@book {MR1088254,
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@article {MR2482128,
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  MRNUMBER = {2425150 (2009f:14044)},
MRREVIEWER = {Oscar G. Villareal},
       DOI = {10.1007/s00208-008-0242-3},
       URL = {http://dx.doi.org/10.1007/s00208-008-0242-3},
}
@misc {arXiv:1608.04547v1,
    AUTHOR = {Habegger, P.},
     TITLE = {Diophantine approximations on definable sets},
      YEAR = {2016},
      NOTE = {\url{arXiv:1608.04547}},
}
<@comment{UPDATE}
@misc {arxiv1611.07287,
   AUTHOR = {Habegger, P.},
    TITLE = {The Norm of {G}aussian Periods},
     YEAR = {2016},
     NOTE = {\url{arXiv:1611.07287}},
}
@comment{UPDATE}
@misc {arxiv2111.01870,
    AUTHOR = {Habegger, Philipp and Schmidt, Harry},
    TITLE = {Lower Bounds for the Canonical Height of a Unicritical Polynomial and Capacity},
     YEAR = {2021},
     NOTE = {\url{arXiv:2111.01870}},
}
@article {MR3034294,
    AUTHOR = {Hacon, Christopher D. and McKernan, James and Xu, Chenyang},
     TITLE = {On the birational automorphisms of varieties of general type},
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  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {177},
      YEAR = {2013},
    NUMBER = {3},
     PAGES = {1077--1111},
      ISSN = {0003-486X},
   MRCLASS = {14E05},
  MRNUMBER = {3034294},
MRREVIEWER = {Alexandr V. Pukhlikov},
       DOI = {10.4007/annals.2013.177.3.6},
       URL = {http://dx.doi.org/10.4007/annals.2013.177.3.6},
}
@article {MR3816072,
    AUTHOR = {Hajli, Mounir},
     TITLE = {On the arithmetic of translated monomial maps},
   JOURNAL = {Funct. Approx. Comment. Math.},
  FJOURNAL = {Uniwersytet im. Adama Mickiewicza w Poznaniu. Wydzia\l 
              Matematyki i Informatyki. Functiones et Approximatio
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    NUMBER = {2},
     PAGES = {177--186},
      ISSN = {0208-6573},
   MRCLASS = {37P30 (11G50 37P15)},
  MRNUMBER = {3816072},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.7169/facm/1667},
       URL = {https://doi.org/10.7169/facm/1667},
}
@article {MR2131425,
    AUTHOR = {Halburd, R. G.},
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  MRNUMBER = {2131425 (2005k:39021)},
       DOI = {10.1088/0305-4470/38/16/L01},
       URL = {http://dx.doi.org/10.1088/0305-4470/38/16/L01},
}

@article {MR1963443,
    AUTHOR = {Halter-Koch, F. and Kone{\v{c}}n{\'a}, P.},
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  MRNUMBER = {MR1963443 (2003m:11047)},
MRREVIEWER = {W. Narkiewicz},
}

@article {MR2001h:11028,
    AUTHOR = {Halter-Koch, F. and Narkiewicz, W.},
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  MRNUMBER = {2001h:11028},
MRREVIEWER = {Liang-Chung Hsia},
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@incollection {kochnarkdynunits97,
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@article {MR1328818,
    AUTHOR = {Halter-Koch, F. and Narkiewicz, W.},
     TITLE = {Polynomial cycles in finitely generated domains},
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  MRNUMBER = {MR1328818 (96d:13035)},
MRREVIEWER = {Jean-Luc Chabert},
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@comment{arxiv1303.6513}
@article {MR3335237,
    AUTHOR = {Hamblen, Spencer and Jones, Rafe and Madhu, Kalyani},
     TITLE = {The density of primes in orbits of {$z^d+c$}},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2015},
    NUMBER = {7},
     PAGES = {1924--1958},
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  MRNUMBER = {3335237},
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       DOI = {10.1093/imrn/rnt349},
       URL = {http://dx.doi.org/10.1093/imrn/rnt349},
}
@comment{UPDATE}
@misc {arxiv2002.01039,
    AUTHOR = {Han, Minsik},
    TITLE = {Gleason-type polynomials for rational maps with nontrivial automorphisms},
     YEAR = {2020},
     NOTE = {\url{arXiv:2002.01039}},
}

@comment{UPDATE}
@misc {arxiv2101.09296,
    AUTHOR = {Han, Minsik},
    TITLE = {Misiurewicz polynomials for rational maps with nontrivial automorphisms II},
     YEAR = {2021},
     NOTE = {\url{arXiv:2101.09296}},
}



@book {MR2445243,
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      NOTE = {Revised by D. R. Heath-Brown and J. H. Silverman,
              With a foreword by Andrew Wiles},
 PUBLISHER = {Oxford University Press},
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     PAGES = {xxii+621},
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  MRNUMBER = {2445243 (2009i:11001)},
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@article {MR0119227,
    AUTHOR = {Harris, Bernard},
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   JOURNAL = {Ann. Math. Statist.},
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  MRNUMBER = {MR0119227 (22 \#9993)},
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@book {MR1416564,
    AUTHOR = {Harris, Joseph},
     TITLE = {Algebraic {G}eometry},
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 PUBLISHER = {Springer-Verlag},
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      YEAR = {1995},
     PAGES = {xx+328},
      ISBN = {0-387-97716-3},
   MRCLASS = {14-01},
  MRNUMBER = {MR1416564 (97e:14001)},
}

@book {hartshorne, 
    AUTHOR = {Hartshorne, Robin},
     TITLE = {Algebraic {G}eometry},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {52},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1977},
     PAGES = {xvi+496},
      ISBN = {0-387-90244-9},
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  MRNUMBER = {MR0463157 (57 \#3116)},
MRREVIEWER = {Robert Speiser},
}
@article {MR2358970,
    AUTHOR = {Hasselblatt, Boris and Propp, James},
     TITLE = {{D}egree-growth of monomial maps},
   JOURNAL = {Ergodic Theory Dynam. Systems},
 FJOURNAL = {Ergodic Theory and Dynamical Systems},
    VOLUME = {27},
      YEAR = {2007},
    NUMBER = {5},
     PAGES = {1375--1397},
      NOTE = {Corrigendum vol. 6, page 1999},
      ISSN = {0143-3857},
   MRCLASS = {37F45 (32H50 37B40)},
  MRNUMBER = {2371607 (2008k:37104b)},
MRREVIEWER = {Mattias Jonsson},
       DOI = {10.1017/S0143385707000685},
       URL = {http://dx.doi.org/10.1017/S0143385707000685},
}
@comment{UPDATE}
@misc {arxiv1309.2562,
    AUTHOR = {Haynes, Alan and White, Christopher},
    TITLE = {Group automorphisms with prescribed growth of periodic
                  points, and small primes in arithmetic progressions
                  in intervals},
     YEAR = {2013},
     NOTE = {\url{arXiv:1309.2562}},
}
@comment{UPDATE}
@misc {arxiv2108.11233,
    AUTHOR = {Healey, Vivian Olsiewski and Hindes, Wade and Jones, Rafe},
    TITLE = {Galois groups and prime divisors in random quadratic sequences},
     YEAR = {2021},
     NOTE = {\url{arXiv:2108.11233}},
}
@comment{arxiv1805.10897}
@article {MR3958050,
    AUTHOR = {Healey, Vivian Olsiewski and Hindes, Wade},
     TITLE = {Stochastic canonical heights},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {201},
      YEAR = {2019},
     PAGES = {228--256},
      ISSN = {0022-314X},
   MRCLASS = {37P15 (11G50 14G05)},
  MRNUMBER = {3958050},
       DOI = {10.1016/j.jnt.2019.02.020},
       URL = {https://doi.org/10.1016/j.jnt.2019.02.020},
}
@comment{arxiv1701.02707}
@article {MR3731313,
    AUTHOR = {Heath-Brown, D. R.},
     TITLE = {I{teration} {of} {quadratic} {polynomials} {over} {finite}
              {fields}},
   JOURNAL = {Mathematika},
  FJOURNAL = {Mathematika. A Journal of Pure and Applied Mathematics},
    VOLUME = {63},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {1041--1059},
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   MRCLASS = {11T06 (11C08 11G20 11Y05 37P05 37P25)},
  MRNUMBER = {3731313},
       URL = {https://doi.org/10.1112/S0025579317000328},
}

@comment{UPDATE}
@misc {arxiv1701.05031,
    AUTHOR = {Heath-Brown, D.R. and Micheli, Giacomo},
    TITLE = {Irreducible polynomials over finite fields produced by composition of quadratics},
     YEAR = {2017},
     NOTE = {\url{arXiv:1701.05031}},
}
@article {MR0422932,
    AUTHOR = {H{\'e}non, M.},
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    NUMBER = {1},
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      ISSN = {0010-3616},
   MRCLASS = {40A05},
  MRNUMBER = {MR0422932 (54 \#10917)},
MRREVIEWER = {P. Fischer},
}
@comment{UPDATE}
@misc {arxiv2102.05041,
    AUTHOR = {Sebastián Herrero and Ricardo Menares and Juan Rivera-Letelier},
    TITLE = {There are at most finitely many singular moduli that are {$S$}-units},
     YEAR = {2021},
     NOTE = {\url{arXiv:2102.05041}},
}
@comment{UPDATE}
@misc {arxiv2102.04865,
    AUTHOR = {Sebastián Herrero and Ricardo Menares and Juan Rivera-Letelier},
    TITLE = {$p$-adic distribution of {CM} points and {H}ecke orbits. {II}: {L}innik equidistribution on the supersingular locus},
     YEAR = {2021},
     NOTE = {\url{arXiv:2102.04865}},
}
@article {MR3869268,
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   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {517},
      YEAR = {2019},
     PAGES = {95--111},
      ISSN = {0021-8693},
   MRCLASS = {37P10 (14J50 14K05 14K22 37A35)},
  MRNUMBER = {3869268},
       DOI = {10.1016/j.jalgebra.2018.09.018},
       URL = {https://doi.org/10.1016/j.jalgebra.2018.09.018},
}
@COMMENT{hermanyoccoz:nonarchdynamics}
@incollection {MR730280,
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MRREVIEWER = {Daniel Barsky},
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}
@book {MR0356988,
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   EDITION = {Second},
 PUBLISHER = {Xerox College Publishing, Lexington, Mass.-Toronto, Ont.},
      YEAR = {1975},
     PAGES = {xi+388},
   MRCLASS = {00A05},
  MRNUMBER = {0356988},
}
@article {MR3230378,
    AUTHOR = {Hidalgo, Rub\'en A.},
     TITLE = {A simple remark on the field of moduli of rational maps},
   JOURNAL = {Q. J. Math.},
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    VOLUME = {65},
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    NUMBER = {2},
     PAGES = {627--635},
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  MRNUMBER = {3230378},
MRREVIEWER = {Ernesto Girondo},
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       URL = {http://dx.doi.org/10.1093/qmath/hat012},
}
@article {MR4295550,
    AUTHOR = {Hidalgo, Ruben A. and Quispe, Sa\'{u}l},
     TITLE = {On real and pseudo-real rational maps},
   JOURNAL = {Nonlinearity},
  FJOURNAL = {Nonlinearity},
    VOLUME = {34},
      YEAR = {2021},
    NUMBER = {9},
     PAGES = {6248--6272},
      ISSN = {0951-7715},
   MRCLASS = {37F46 (37P45)},
  MRNUMBER = {4295550},
       DOI = {10.1088/1361-6544/ac12ad},
       URL = {https://doi.org/10.1088/1361-6544/ac12ad},
}
@article {MR3062913,
    AUTHOR = {Hindes, Wade},
     TITLE = {Points on elliptic curves parametrizing dynamical {G}alois
              groups},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {159},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {149--167},
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     CODEN = {AARIA9},
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  MRNUMBER = {3062913},
       DOI = {10.4064/aa159-2-5},
       URL = {http://dx.doi.org/10.4064/aa159-2-5},
}
@article {MR3283185,
    AUTHOR = {Hindes, Wade},
     TITLE = {Galois uniformity in quadratic dynamics over {$k(t)$}},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {148},
      YEAR = {2015},
     PAGES = {372--383},
      ISSN = {0022-314X},
   MRCLASS = {37P55 (11R32 12F10 14G05)},
  MRNUMBER = {3283185},
       DOI = {10.1016/j.jnt.2014.09.033},
       URL = {http://dx.doi.org/10.1016/j.jnt.2014.09.033},
}
@article {MR3390253,
    AUTHOR = {Hindes, Wade},
     TITLE = {Rational points on certain families of symmetric equations},
   JOURNAL = {Int. J. Number Theory},
  FJOURNAL = {International Journal of Number Theory},
    VOLUME = {11},
      YEAR = {2015},
    NUMBER = {6},
     PAGES = {1821--1838},
      ISSN = {1793-0421},
   MRCLASS = {14G05 (37P55)},
  MRNUMBER = {3390253},
       DOI = {10.1142/S1793042115500797},
       URL = {http://dx.doi.org/10.1142/S1793042115500797},
}
@article {MR3353265,
    AUTHOR = {Hindes, Wade},
     TITLE = {The arithmetic of curves defined by iteration},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {169},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {1--27},
      ISSN = {0065-1036},
   MRCLASS = {14G05 (37P55)},
  MRNUMBER = {3353265},
       DOI = {10.4064/aa169-1-1},
       URL = {http://dx.doi.org/10.4064/aa169-1-1},
}
@comment{arxiv1504.08334}
@article {MR3608948,
    AUTHOR = {Hindes, Wade},
     TITLE = {Prime divisors in polynomial orbits over function fields},
   JOURNAL = {Bull. Lond. Math. Soc.},
  FJOURNAL = {Bulletin of the London Mathematical Society},
    VOLUME = {48},
      YEAR = {2016},
    NUMBER = {6},
     PAGES = {1029--1036},
      ISSN = {0024-6093},
   MRCLASS = {14H05 (11R32 14G05 14H25 37P55)},
  MRNUMBER = {3608948},
MRREVIEWER = {Yu Yasufuku},
       URL = {https://doi.org/10.1112/blms/bdw061},
}
@comment{arxiv1509.00752}
@article {MR3963978,
    AUTHOR = {Hindes, Wade},
     TITLE = {The average number of integral points in orbits},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {26},
      YEAR = {2019},
    NUMBER = {1},
     PAGES = {101--120},
      ISSN = {1073-2780},
   MRCLASS = {37P45 (11B37)},
  MRNUMBER = {3963978},
MRREVIEWER = {Simone Ugolini},
       DOI = {10.4310/MRL.2019.v26.n1.a7},
       URL = {https://doi.org/10.4310/MRL.2019.v26.n1.a7},
}
@comment{UPDATE}
@misc {arxiv2002.09798,
    AUTHOR = {Hindes, Wade},
    TITLE = {Dynamical height growth: left, right, and total orbits},
     YEAR = {2020},
     NOTE = {\url{arXiv:2002.09798}},
}
@comment{UPDATE}
@misc {arxiv2012.14960,
    AUTHOR = {Hindes, Wade},
    TITLE = {Orbit counting in polarized dynamical systems},
     YEAR = {2020},
     NOTE = {\url{arXiv:2012.14960}},
}

@comment{UPDATE}
@misc {arxiv2209.09182,
    AUTHOR = {Hindes, Wade},
    TITLE = {Dynamical {D}iophantine Approximation Exponents in Characteristic $p$},
     YEAR = {2022},
     NOTE = {\url{arXiv:2209.09182}},
}


@comment{arxiv1603.04459}
@article {MR3814334,
    AUTHOR = {Hindes, Wade},
     TITLE = {Average {Z}sigmondy sets, dynamical {G}alois groups, and the
              {K}odaira-{S}pencer map},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {370},
      YEAR = {2018},
    NUMBER = {9},
     PAGES = {6391--6410},
      ISSN = {0002-9947},
   MRCLASS = {37P15 (11B37 11G99 11R32 14G05)},
  MRNUMBER = {3814334},
       DOI = {10.1090/tran/7125},
       URL = {https://doi.org/10.1090/tran/7125},
}
@comment{UPDATE}
@misc {arxiv1610.01964,
    AUTHOR = {Hindes, Wade},
    TITLE = {Integrality estimates in orbits over function fields},
     YEAR = {2016},
     NOTE = {\url{arXiv:1610.01964}},
}
@comment{UPDATE}
@misc {arxiv1705.08353,
    AUTHOR = {Hindes, Wade},
    TITLE = {Classifying {G}alois groups of small iterates via rational points},
     YEAR = {2017},
     NOTE = {\url{arXiv:1705.08353}},
}
@comment{UPDATE}
@misc {arxiv2006.08563,
    AUTHOR = {Hindes, Wade},
    TITLE = {Counting points of bounded height in monoid orbits},
     YEAR = {2020},
     NOTE = {\url{arXiv:2006.08563}},
}
@comment{arxiv1708.06014}
@article {MR3746988,
    AUTHOR = {Hindes, Wade},
     TITLE = {Galois groups of some iterated polynomials over cyclotomic
              extensions},
   JOURNAL = {Arch. Math. (Basel)},
  FJOURNAL = {Archiv der Mathematik},
    VOLUME = {110},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {109--113},
      ISSN = {0003-889X},
   MRCLASS = {11R32 (37P15)},
  MRNUMBER = {3746988},
       DOI = {10.1007/s00013-017-1120-6},
       URL = {https://doi.org/10.1007/s00013-017-1120-6},
}
@comment{arxiv1810.02269}
@article {MR3994153,
    AUTHOR = {Hindes, Wade},
     TITLE = {Finite orbit points for sets of quadratic polynomials},
   JOURNAL = {Int. J. Number Theory},
  FJOURNAL = {International Journal of Number Theory},
    VOLUME = {15},
      YEAR = {2019},
    NUMBER = {8},
     PAGES = {1693--1719},
      ISSN = {1793-0421},
   MRCLASS = {37P05 (37P30 37P35)},
  MRNUMBER = {3994153},
MRREVIEWER = {Solomon Vishkautsan},
       DOI = {10.1142/S1793042119500945},
       URL = {https://doi.org/10.1142/S1793042119500945},
}
@comment{UPDATE}
@misc {arxiv1904.04709,
    AUTHOR = {Hindes, Wade},
    TITLE = {Dynamical and arithmetic degrees for random iterations of maps on projective space},
     YEAR = {2018},
     NOTE = {\url{arXiv:1904.04709}},
}
@comment{UPDATE}
@misc {arxiv2208.03856,
    AUTHOR = {Hindes, Wade and Jacobs, Reiyah and Ye, Peter},
    TITLE = {Irreducible polynomials in quadratic semigroups},
     YEAR = {2022},
     NOTE = {\url{arXiv:2208.03856}},
}

@comment{arxiv1710.04332}
@article {MR4068273,
    AUTHOR = {Hindes, Wade and Jones, Rafe},
     TITLE = {Riccati equations and polynomial dynamics over function
              fields},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {373},
      YEAR = {2020},
    NUMBER = {3},
     PAGES = {1555--1575},
      ISSN = {0002-9947},
   MRCLASS = {11R32 (14G05 37P15)},
  MRNUMBER = {4068273},
       DOI = {10.1090/tran/7855},
       URL = {https://doi.org/10.1090/tran/7855},
}

@misc {hindrynotesonlocalheights,
    AUTHOR = {Hindry, Marc},
     TITLE = {Sur les hauteurs locales de {N}{\'e}ron sur les vari{\'e}t{\'e}s ab{\'e}liennes},
      NOTE = {Pr{\'e}publications Math{\'e}matiques de l'U.R.A. 212 'Th{\'e}ories G{\'e}om{\'e}triques' no. 51, Universit{\'e} Paris 7 1993},
       URL = {https://webusers.imj-prg.fr/~marc.hindry/Neron.pdf},
}

@book {hindrysilverman:diophantinegeometry,
    AUTHOR = {Hindry, Marc and Silverman, Joseph H.},
     TITLE = {Diophantine {G}eometry: An {I}ntroduction},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {201},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {2000},
     PAGES = {xiv+558},
      ISBN = {0-387-98975-7; 0-387-98981-1},
   MRCLASS = {11Gxx (11-02 11G10 11G30 11G50 14G25)},
  MRNUMBER = {MR1745599 (2001e:11058)},
MRREVIEWER = {Dino J. Lorenzini},
}

@article {hindrysilverman:integralpts,
    AUTHOR = {Hindry, Marc and Silverman, Joseph H.},
     TITLE = {The canonical height and integral points on elliptic curves},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {93},
      YEAR = {1988},
    NUMBER = {2},
     PAGES = {419--450},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11G05 (11D25 14G25)},
  MRNUMBER = {MR948108 (89k:11044)},
MRREVIEWER = {Ernst-Ulrich Gekeler},
}

@article {hindrysilverman:torsionpoints,
    AUTHOR = {Hindry, Marc and Silverman, Joseph H.},
     TITLE = {Sur le nombre de points de torsion rationnels sur une courbe
              elliptique},
   JOURNAL = {C.~R.~Acad. Sci. Paris S\'er. I Math.},
  FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
              Math\'ematique},
    VOLUME = {329},
      YEAR = {1999},
    NUMBER = {2},
     PAGES = {97--100},
      ISSN = {0764-4442},
     CODEN = {CASMEI},
   MRCLASS = {11G05 (11G50 14G05)},
  MRNUMBER = {MR1710502 (2000g:11047)},
MRREVIEWER = {Carlo Gasbarri},
}
@incollection {hindrysilverman:lehmer, 
    AUTHOR = {Hindry, Marc and Silverman, Joseph H.},
     TITLE = {On {L}ehmer's conjecture for elliptic curves},
 BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres, Paris 1988--1989},
    SERIES = {Progr. Math.},
    VOLUME = {91},
     PAGES = {103--116},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {1990},
   MRCLASS = {11G05 (14G25)},
  MRNUMBER = {MR1104702 (92e:11062)},
MRREVIEWER = {Philippe Satg{\'e}},
}
@comment{UPDATE}
@misc {arxiv1602.07378,
    AUTHOR = {Hironaka, Eriko and Koch, Sarah},
    TITLE = {A disconnected deformation space of rational maps},
     YEAR = {2016},
     NOTE = {\url{arXiv:1602.07378}},
}
@comment{UPDATE}
@misc {arxiv2108.03520,
    AUTHOR = {Hoey, Alexandra and Iskander, Jonas and Jin, Steven and Trejos Su{\'a}rez,  Fernando},
    TITLE = { unconditional explicit bound on the error term in the {S}ato--{T}ate conjecture},
     YEAR = {2021},
     NOTE = {\url{arXiv:2108.03520}},
}
@article {MR946432,
    AUTHOR = {Hoffman, Michael E. and Withers, William Douglas},
     TITLE = {Generalized {C}hebyshev polynomials associated with affine
              {W}eyl groups},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {308},
      YEAR = {1988},
    NUMBER = {1},
     PAGES = {91--104},
      ISSN = {0002-9947},
   MRCLASS = {33A65 (42C05 58F13)},
  MRNUMBER = {946432},
MRREVIEWER = {Walter Schempp},
       DOI = {10.2307/2000951},
       URL = {https://doi.org/10.2307/2000951},
}
@comment{UPDATE}
@misc {arxiv1609.06696,
    AUTHOR = {Holden, Joshua and Richardson, Pamela A.  and Robinson, Margaret M.},
    TITLE = {Counting fixed points and two-cycles of the sigular map
                  $x\mapsto x^{x^n}$ modulo powers of a prime},
     YEAR = {2016},
     NOTE = {\url{arXiv:1609.06696}},
}
@article {arxiv1105.5346,
    AUTHOR = {Holden, Joshua and Robinson, Margaret M.},
     TITLE = {Counting fixed points, two-cycles, and collisions of the
              discrete exponential function using {$p$}-adic methods},
   JOURNAL = {J. Aust. Math. Soc.},
  FJOURNAL = {Journal of the Australian Mathematical Society},
    VOLUME = {92},
      YEAR = {2012},
    NUMBER = {2},
     PAGES = {163--178},
      ISSN = {1446-7887},
   MRCLASS = {11D88 (11A07 11N37 11Y16 94A60)},
  MRNUMBER = {2999154},
MRREVIEWER = {R. A. Mollin},
       DOI = {10.1017/S1446788712000262},
       URL = {http://dx.doi.org/10.1017/S1446788712000262},
}
@comment{UPDATE}
@misc {arxiv1907.05204,
    AUTHOR = {Hone, A. N. W.},
    TITLE = {Continued fractions and Hankel determinants from hyperelliptic curves},
     YEAR = {2019},
     NOTE = {\url{arXiv:1907.05204}},
}
@article {MR2212057,
    AUTHOR = {Hone, A. N. W.},
     TITLE = {Diophantine non-integrability of a third-order recurrence with
              the {L}aurent property},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {39},
      YEAR = {2006},
    NUMBER = {12},
     PAGES = {L171--L177},
      ISSN = {0305-4470},
     CODEN = {JPHAC5},
   MRCLASS = {11B37 (11D25 37C99 37F99)},
  MRNUMBER = {2212057 (2006j:11017)},
       DOI = {10.1088/0305-4470/39/12/L01},
       URL = {http://dx.doi.org/10.1088/0305-4470/39/12/L01},
}

@article {hsia:weakneronmodel,
    AUTHOR = {Hsia, Liang-Chung},
     TITLE = {A weak {N}\'eron model with applications to {$p$}-adic
              dynamical systems},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {100},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {277--304},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {14G20 (14E99)},
  MRNUMBER = {MR1387667 (97j:14024)},
MRREVIEWER = {Guido Van Steen},
}

@article {hsia:periodicpoint,
    AUTHOR = {Hsia, Liang-Chung},
     TITLE = {Closure of periodic points over a non-{A}rchimedean field},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {62},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {685--700},
      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {11S80 (37F10 37F50)},
  MRNUMBER = {MR1794277 (2001j:11117)},
MRREVIEWER = {Michael E. Zieve},
}

@article {hsia:dynamicalzeta,
    AUTHOR = {Hsia, Liang-Chung},
     TITLE = {On the dynamical height zeta functions},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {63},
      YEAR = {1997},
    NUMBER = {1},
     PAGES = {146--169},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11G30 (11M45 14G10)},
  MRNUMBER = {MR1438655 (99c:11076)},
MRREVIEWER = {Emmanuel Peyre},
}

@UNPUBLISHED{hsia:padicequidist,
   AUTHOR  = {Hsia, Liang-Chung},
   TITLE   = {$p$-adic equidistribution theorems},
   NOTE    = {manuscript},
   YEAR    = {2003},
}

@article {hsia:drinfeld,
    AUTHOR = {Hsia, Liang-Chung},
     TITLE = {On the reduction of a non-torsion point of a {D}rinfeld
              module},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {128},
      YEAR = {2008},
    NUMBER = {6},
     PAGES = {1458--1484},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11G09},
  MRNUMBER = {MR2419173 (2009f:11065)},
MRREVIEWER = {Ambrus P{\'a}l},
}
@comment{UPDATE}
@misc {arxiv1502.06815,
    AUTHOR = {Hsia, Liang-Chung and Li, Hua-Chieh },
    TITLE = {Ramification Filtrations of Certain Abelian Lie
                  Extensions of Local Fields},
     YEAR = {2015},
     NOTE = {\url{arXiv:1502.06815}},
}
@article {MR2537714,
    AUTHOR = {Hsia, Liang-Chung and Silverman, Joseph},
     TITLE = {On a dynamical {B}rauer-{M}anin obstruction},
   JOURNAL = {J. Th\'eor. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
    VOLUME = {21},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {235--250},
      ISSN = {1246-7405},
   MRCLASS = {37Pxx (11R04)},
  MRNUMBER = {MR2537714},
}
@comment{arxiv0910.4498}
@article {MR2782672,
    AUTHOR = {Hsia, Liang-Chung and Silverman, Joseph H.},
     TITLE = {A quantitative estimate for quasiintegral points in orbits},
   JOURNAL = {Pacific J. Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {249},
      YEAR = {2011},
    NUMBER = {2},
     PAGES = {321--342},
      ISSN = {0030-8730},
     CODEN = {PJMAAI},
   MRCLASS = {37P15 (11B37 14Gxx)},
  MRNUMBER = {2782672},
       DOI = {10.2140/pjm.2011.249.321},
       URL = {http://dx.doi.org/10.2140/pjm.2011.249.321},
}
@comment{UPDATE}
@misc {arxiv1810.03841,
    AUTHOR = {Hsia, Liang-Chung and Kawaguchi, Shu},
    TITLE = {Heights and periodic points for one-parameter families of {H}{\'e}non maps},
     YEAR = {2018},
     NOTE = {\url{arXiv:1810.03841}},
}
@article {MR3687102,
    AUTHOR = {Hsia, Liang-Chung and Tucker, Thomas J.},
     TITLE = {Greatest common divisors of iterates of polynomials},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {11},
      YEAR = {2017},
    NUMBER = {6},
     PAGES = {1437--1459},
      ISSN = {1937-0652},
   MRCLASS = {37P05 (11B83 14G25)},
  MRNUMBER = {3687102},
       URL = {https://doi.org/10.2140/ant.2017.11.1437},
}
@article {MR4017540,
    AUTHOR = {Hu, Fei},
     TITLE = {Cohomological and numerical dynamical degrees on abelian
              varieties},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {13},
      YEAR = {2019},
    NUMBER = {8},
     PAGES = {1941--1958},
      ISSN = {1937-0652},
   MRCLASS = {14G17 (14K05 16K20 37P55)},
  MRNUMBER = {4017540},
       DOI = {10.2140/ant.2019.13.1941},
       URL = {https://doi.org/10.2140/ant.2019.13.1941},
}
@comment{UPDATE}
@misc {arxiv2102.04405,
    AUTHOR = {Hu, Fei and Truong, Tuyen Trung},
    TITLE = {A unification of various conjectures related to algebraic cycles, {W}eil cohomology theories, and dynamical degrees},
     YEAR = {2021},
     NOTE = {\url{arXiv:2102.04405}},
}
@book {MR665428,
    AUTHOR = {Hua, Loo Keng},
     TITLE = {Introduction to {N}umber {T}heory},
      NOTE = {Translated from the Chinese by Peter Shiu},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1982},
     PAGES = {xviii+572},
      ISBN = {3-540-10818-1},
   MRCLASS = {10-01},
  MRNUMBER = {MR665428 (83f:10001)},
}
@misc {arxiv1702.03881,
    AUTHOR = {Huang, Keping},
    TITLE = {Generalized Greatest Common Divisors for the Orbits under Rational Functions},
     YEAR = {2017},
     NOTE = {\url{arXiv:1702.03881 }},
}
@misc {arxiv1808.02849,
    AUTHOR = {Huang, Keping},
    TITLE = {A Gap Principle for Subvarieties with Finitely Many Periodic Points},
     YEAR = {2018},
     NOTE = {\url{arXiv:1808.02849}},
}
@misc {arxiv1908.06231,
    AUTHOR = {Huang, Keping},
    TITLE = {Uniform Bounds for Periods of Endomorphisms of Varieties},
     YEAR = {2019},
     NOTE = {\url{arXiv:1908.06231}},
}
@incollection {hubbard:henonmap,
    AUTHOR = {Hubbard, John},
     TITLE = {The {H}\'enon mapping in the complex domain},
 BOOKTITLE = {Chaotic {D}ynamics and {F}ractals (Atlanta, Ga., 1985)},
    SERIES = {Notes Rep. Math. Sci. Engrg.},
    VOLUME = {2},
     PAGES = {101--111},
 PUBLISHER = {Academic Press},
   ADDRESS = {Orlando, FL},
      YEAR = {1986},
   MRCLASS = {58F11 (30D05)},
  MRNUMBER = {MR858009},
}
@article {MR1275463,
    AUTHOR = {Hubbard, John H. and Papadopol, Peter},
     TITLE = {Superattractive fixed points in {$\textbf{C}^n$}},
   JOURNAL = {Indiana Univ. Math. J.},
  FJOURNAL = {Indiana University Mathematics Journal},
    VOLUME = {43},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {321--365},
      ISSN = {0022-2518},
   MRCLASS = {32H50 (32C30)},
  MRNUMBER = {1275463},
MRREVIEWER = {Gregery T. Buzzard},
       DOI = {10.1512/iumj.1994.43.43014},
       URL = {https://doi.org/10.1512/iumj.1994.43.43014},
}
@article {MR1768111,
    AUTHOR = {Hubbard, John and Papadopol, Peter and Veselov, Vladimir},
     TITLE = {A compactification of {H}\'enon mappings in {$\mathbb{C}\sp 2$}
              as dynamical systems},
   JOURNAL = {Acta Math.},
  FJOURNAL = {Acta Mathematica},
    VOLUME = {184},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {203--270},
      ISSN = {0001-5962},
     CODEN = {ACMAA8},
   MRCLASS = {37F10 (32H50)},
  MRNUMBER = {MR1768111 (2001f:37056)},
MRREVIEWER = {Adrien Douady},
}

@incollection {MR1315537,
    AUTHOR = {Hubbard, John and Schleicher, Dierk},
     TITLE = {The spider algorithm},
 BOOKTITLE = {Complex {D}ynamical {S}ystems (Cincinnati, OH, 1994)},
    SERIES = {Proc. Sympos. Appl. Math.},
    VOLUME = {49},
     PAGES = {155--180},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1994},
   MRCLASS = {58F23 (30D05)},
  MRNUMBER = {MR1315537},
}
@comment{UPDATE}
@misc {arxiv1906.04514,
    AUTHOR = {Huguin, Valentin},
    TITLE = {Simultaneously preperiodic integers for quadratic polynomials},
     YEAR = {2019},
     NOTE = {\url{arXiv:1906.04514}},
}
@comment{UPDATE}
@misc {arxiv2009.02422,
    AUTHOR = {Huguin, Valentin},
    TITLE = {Unicritical polynomial maps with rational multipliers},
     YEAR = {2020},
     NOTE = {\url{arXiv:2009.02422}},
}
@comment{UPDATE}
@misc {arxiv2107.07262,
    AUTHOR = {Huguin, Valentin},
    TITLE = {Quadratic rational maps with integer multipliers},
     YEAR = {2021},
     NOTE = {\url{arXiv:2107.07262}},
}

@phdthesis{hutz:thesis, 
    AUTHOR = {Hutz, Benjamin},
     TITLE = {Arithmetic Dynamics on Varieties in Dimension Greater Than One},
   SCHOOL = {Brown University},
     YEAR = {2007}
}
@comment{UPDATE}
@misc {arxiv:0801.3648,
    AUTHOR = {Hutz, Benjamin},
    TITLE = {A Computational Investigation of {W}ehler {K}3 Surfaces},
     YEAR = {2008},
     NOTE = {\url{arXiv:0801.3648}},
}
@article {MR2772404,
    AUTHOR = {Hutz, Benjamin},
     TITLE = {Finding rational periodic points on {W}ehler {$K3$} surfaces},
   JOURNAL = {New Zealand J. Math.},
  FJOURNAL = {New Zealand Journal of Mathematics},
    VOLUME = {39},
      YEAR = {2009},
     PAGES = {133--141},
      ISSN = {1171-6096},
   MRCLASS = {11G05 (14J28 37Pxx)},
  MRNUMBER = {2772404},
}
@comment{arxiv:0801.3645}
@article {MR2741181,
    AUTHOR = {Hutz, Benjamin},
     TITLE = {Good reduction of periodic points on projective varieties},
   JOURNAL = {Illinois J. Math.},
  FJOURNAL = {Illinois Journal of Mathematics},
    VOLUME = {53},
      YEAR = {2009},
    NUMBER = {4},
     PAGES = {1109--1126},
      ISSN = {0019-2082},
     CODEN = {IJMTAW},
   MRCLASS = {37Pxx (11G05 14G99)},
  MRNUMBER = {2741181},
       URL = {http://projecteuclid.org/getRecord?id=euclid.ijm/1290435342},
}

@article {arxiv:0801.3643,
    AUTHOR = {Hutz, Benjamin},
     TITLE = {Dynatomic cycles for morphisms of projective varieties},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {16},
      YEAR = {2010},
     PAGES = {125--159},
      ISSN = {1076-9803},
   MRCLASS = {14Gxx (11G99 37Pxx)},
  MRNUMBER = {2657371},
}
@article {arxiv:0811.3225,
    AUTHOR = {Hutz, Benjamin},
     TITLE = {Rational periodic points for degree two polynomial morphisms
              on projective space},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {141},
      YEAR = {2010},
    NUMBER = {3},
     PAGES = {275--288},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {37Pxx},
  MRNUMBER = {2587288},
       DOI = {10.4064/aa141-3-3},
       URL = {http://dx.doi.org/10.4064/aa141-3-3},
}
@article {arxiv:1011.5155,
    AUTHOR = {Hutz, Benjamin},
     TITLE = {Effectivity of dynatomic cycles for morphisms of projective
              varieties using deformation theory},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {140},
      YEAR = {2012},
    NUMBER = {10},
     PAGES = {3507--3514},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {37P55 (37P35)},
  MRNUMBER = {2929019},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.1090/S0002-9939-2012-11192-X},
       URL = {http://dx.doi.org/10.1090/S0002-9939-2012-11192-X},
}
@comment{arxiv1210.6246}
@article {MR3266961,
    AUTHOR = {Hutz, Benjamin},
     TITLE = {Determination of all rational preperiodic points for morphisms
              of $\mathbb{P}^{N}$},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {84},
      YEAR = {2015},
    NUMBER = {291},
     PAGES = {289--308},
      ISSN = {0025-5718},
   MRCLASS = {37Pxx},
  MRNUMBER = {3266961},
       DOI = {10.1090/S0025-5718-2014-02850-0},
       URL = {http://dx.doi.org/10.1090/S0025-5718-2014-02850-0},
}
@comment{UPDATE}
@misc {arxiv:1908.03184,
    AUTHOR = {Hutz, Benjamin},
    TITLE = {Multipliers and invariants of endomorphisms of projective space in dimension greater than 1},
     YEAR = {2019},
     NOTE = {\url{arXiv:1908.03184}},
}


@article {arxiv1007.0744,
    AUTHOR = {Hutz, Benjamin and Hyde, Trevor and Krause, Benjamin},
     TITLE = {Preimages of quadratic dynamical systems},
   JOURNAL = {Involve},
  FJOURNAL = {Involve. A Journal of Mathematics},
    VOLUME = {4},
      YEAR = {2011},
    NUMBER = {4},
     PAGES = {343--363},
      ISSN = {1944-4176},
   MRCLASS = {37P05 (14G05)},
  MRNUMBER = {2905234},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.2140/involve.2011.4.343},
       URL = {http://dx.doi.org/10.2140/involve.2011.4.343},
}
@comment{\url{arXiv:0909.5050} Superceded by the following paper}
@article {MR3065461,
    AUTHOR = {Hutz, Benjamin and Ingram, Patrick},
     TITLE = {On {P}oonen's conjecture concerning rational preperiodic
              points of quadratic maps},
   JOURNAL = {Rocky Mountain J. Math.},
  FJOURNAL = {The Rocky Mountain Journal of Mathematics},
    VOLUME = {43},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {193--204},
      ISSN = {0035-7596},
   MRCLASS = {11G05},
  MRNUMBER = {3065461},
MRREVIEWER = {Jasbir Singh Chahal},
       DOI = {10.1216/RMJ-2013-43-1-193},
       URL = {https://doi.org/10.1216/RMJ-2013-43-1-193},
}
@comment{arxiv1309.6696}
@article {MR3309942,
    AUTHOR = {Hutz, Benjamin and Manes, Michelle},
     TITLE = {The field of definition for dynamical systems on {$\mathbb P^N$}},
   JOURNAL = {Bull. Inst. Math. Acad. Sin. (N.S.)},
  FJOURNAL = {Bulletin of the Institute of Mathematics. Academia Sinica. New
              Series},
    VOLUME = {9},
      YEAR = {2014},
    NUMBER = {4},
     PAGES = {585--601},
      ISSN = {2304-7909},
   MRCLASS = {37P45 (11R34 14J10)},
  MRNUMBER = {3309942},
MRREVIEWER = {Joseph H. Silverman},
}
@comment{arxiv:1805.08579}
@article {MR3956143,
    AUTHOR = {Hutz, Benjamin and Stoll, Michael},
     TITLE = {Smallest representatives of {$\operatorname{SL}(2,\mathbb{Z})$}-orbits of
              binary forms and endomorphisms of {$\mathbb{P}^1$}},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {189},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {283--308},
      ISSN = {0065-1036},
   MRCLASS = {37P05 (11C08 11Y99 37P45)},
  MRNUMBER = {3956143},
       DOI = {10.4064/aa180618-9-12},
       URL = {https://doi.org/10.4064/aa180618-9-12},
}
@comment{arxiv1105.1696}
@article {MR3145344,
    AUTHOR = {Hutz, Benjamin and Szpiro, Lucien},
     TITLE = {Almost {N}ewton, sometimes {L}att\`es},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {136},
      YEAR = {2014},
     PAGES = {423--437},
      ISSN = {0022-314X},
   MRCLASS = {37P05 (14H52 37P45)},
  MRNUMBER = {3145344},
       DOI = {10.1016/j.jnt.2013.10.004},
       URL = {https://doi.org/10.1016/j.jnt.2013.10.004},
}
@comment{arxiv1110.5082}
@article {MR3136590,
    AUTHOR = {Hutz, Benjamin and Tepper, Michael},
     TITLE = {Multiplier spectra and the moduli space of degree 3 morphisms
              on {$\mathbb{P}^1$}},
   JOURNAL = {JP J. Algebra Number Theory Appl.},
  FJOURNAL = {JP Journal of Algebra, Number Theory and Applications},
    VOLUME = {29},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {189--206},
      ISSN = {0972-5555},
   MRCLASS = {32G15 (37P05 37P45)},
  MRNUMBER = {3136590},
}
@comment{arxiv1309.4048}
@article {MR3358544,
    AUTHOR = {Hutz, Benjamin and Towsley, Adam},
     TITLE = {Misiurewicz points for polynomial maps and transversality},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {21},
      YEAR = {2015},
     PAGES = {297--319},
   MRCLASS = {37P05 (11B83 37P35 37P45)},
  MRNUMBER = {3358544},
MRREVIEWER = {Rafe Jones},
       URL = {http://nyjm.albany.edu:8000/j/2015/21_297.html},
}
@incollection {MR1963562,
    AUTHOR = {Huybrechts, Daniel},
     TITLE = {Compact hyperk{\"a}hler manifolds},
 BOOKTITLE = {Calabi-{Y}au manifolds and related geometries ({N}ordfjordeid,
              2001)},
    SERIES = {Universitext},
     PAGES = {161--225},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2003},
   MRCLASS = {53C26},
  MRNUMBER = {MR1963562},
}

@comment{--III-- }

@comment{arxiv0805.1554}
@article {MR2679454,
    AUTHOR = {Ih, Su-Ion and Tucker, Thomas J.},
     TITLE = {A finiteness property for preperiodic points of {C}hebyshev
              polynomials},
   JOURNAL = {Int. J. Number Theory},
  FJOURNAL = {International Journal of Number Theory},
    VOLUME = {6},
      YEAR = {2010},
    NUMBER = {5},
     PAGES = {1011--1025},
      ISSN = {1793-0421},
   MRCLASS = {11G05 (11G35 11J71 11J86 33C45)},
  MRNUMBER = {2679454},
       DOI = {10.1142/S1793042110003356},
       URL = {http://dx.doi.org/10.1142/S1793042110003356},
}
@article {MR2769080,
    AUTHOR = {Ih, Su-ion},
     TITLE = {A nondensity property of preperiodic points on {C}hebyshev
              dynamical systems},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {131},
      YEAR = {2011},
    NUMBER = {4},
     PAGES = {750--780},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {37Pxx (11G05 11J71 14Gxx 37Fxx)},
  MRNUMBER = {2769080},
       DOI = {10.1016/j.jnt.2010.10.003},
       URL = {http://dx.doi.org/10.1016/j.jnt.2010.10.003},
}
@book {MR637060,
    AUTHOR = {Iitaka, Shigeru},
     TITLE = {Algebraic geometry},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {76},
      NOTE = {An introduction to birational geometry of algebraic varieties,
              North-Holland Mathematical Library, 24},
 PUBLISHER = {Springer-Verlag, New York-Berlin},
      YEAR = {1982},
     PAGES = {x+357},
      ISBN = {0-387-90546-4},
   MRCLASS = {14-01 (14-02 14E05)},
  MRNUMBER = {637060 (84j:14001)},
MRREVIEWER = {Werner Kleinert},
}

@comment{UPDATE}
@misc {arxiv2008.01222,
    AUTHOR = {Illig, Peter and Jones, Rafe and Orvis, Eli and Segawa,
                  Yukihiko and Spinale, Nick},
    TITLE = {Newly reducible polynomial iterates},
     YEAR = {2020},
     NOTE = {\url{arXiv:2008.01222}},
}


@article {MR3492630,
    AUTHOR = {Ingram, Patrick},
     TITLE = {Rigidity and height bounds for certain post-critically finite
              endomorphisms of {$\mathbb{P}^N$}},
   JOURNAL = {Canad. J. Math.},
  FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de
              Math\'{e}matiques},
    VOLUME = {68},
      YEAR = {2016},
    NUMBER = {3},
     PAGES = {625--654},
      ISSN = {0008-414X},
   MRCLASS = {37P15 (32H50 37P30)},
  MRNUMBER = {3492630},
MRREVIEWER = {Dragos Ghioca},
       DOI = {10.4153/CJM-2015-045-x},
       URL = {https://doi.org/10.4153/CJM-2015-045-x},
}
@article {MR3257554,
    AUTHOR = {Ingram, Patrick},
     TITLE = {A lower bound for the canonical height associated to a
              {D}rinfeld module},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2014},
    NUMBER = {17},
     PAGES = {4879--4916},
      ISSN = {1073-7928},
   MRCLASS = {11G09},
  MRNUMBER = {3257554},
MRREVIEWER = {Yu Yasufuku},
       DOI = {10.1093/imrn/rnt104},
       URL = {https://doi.org/10.1093/imrn/rnt104},
}


@article {MR3988672,
    AUTHOR = {Ingram, Patrick},
     TITLE = {Canonical heights and preperiodic points for certain weighted
              homogeneous families of polynomials},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2019},
    NUMBER = {15},
     PAGES = {4859--4879},
      ISSN = {1073-7928},
   MRCLASS = {37P05 (37P30)},
  MRNUMBER = {3988672},
MRREVIEWER = {Benjamin A. Hutz},
       DOI = {10.1093/imrn/rnx291},
       URL = {https://doi.org/10.1093/imrn/rnx291},
}
@article {MR2504779,
    AUTHOR = {Ingram, Patrick},
     TITLE = {Lower bounds on the canonical height associated to the
              morphism {$\phi(z)=z^d+c$}},
   JOURNAL = {Monatsh. Math.},
  FJOURNAL = {Monatshefte f\"ur Mathematik},
    VOLUME = {157},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {69--89},
      ISSN = {0026-9255},
     CODEN = {MNMTA2},
   MRCLASS = {11G50 (37F10 37P30)},
  MRNUMBER = {MR2504779 (2010a:11122)},
MRREVIEWER = {Niko Naumann},
       DOI = {10.1007/s00605-008-0018-6},
       URL = {http://dx.doi.org/10.1007/s00605-008-0018-6},
}
@article {MR2605536,
    AUTHOR = {Ingram, Patrick},
     TITLE = {A quantitative primitive divisor result for points on elliptic
              curves},
   JOURNAL = {J. Th\'eor. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
    VOLUME = {21},
      YEAR = {2009},
    NUMBER = {3},
     PAGES = {609--634},
      ISSN = {1246-7405},
   MRCLASS = {11G05 (11G50)},
  MRNUMBER = {2605536 (2011d:11129)},
MRREVIEWER = {Yann Bugeaud},
}
		
@comment{arxiv1003.4225}
@article {MR3181564,
    AUTHOR = {Ingram, Patrick},
     TITLE = {Variation of the canonical height for a family of polynomials},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {685},
      YEAR = {2013},
     PAGES = {73--97},
      ISSN = {0075-4102},
   MRCLASS = {37P05 (11G50 14G40 37P15 37P30)},
  MRNUMBER = {3181564},
MRREVIEWER = {Joseph H. Silverman},
}

@article {arxiv1010.3393,
    AUTHOR = {Ingram, Patrick},
     TITLE = {A finiteness result for post-critically finite polynomials},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2012},
    NUMBER = {3},
     PAGES = {524--543},
      ISSN = {1073-7928},
   MRCLASS = {37P05 (37P30)},
  MRNUMBER = {2885981},
MRREVIEWER = {Peter Ha{\"{\i}}ssinsky},
}
@comment{arxiv1111.3607}
@article {MR3064415,
    AUTHOR = {Ingram, Patrick},
     TITLE = {Arboreal {G}alois representations and uniformization of
              polynomial dynamics},
   JOURNAL = {Bull. Lond. Math. Soc.},
  FJOURNAL = {Bulletin of the London Mathematical Society},
    VOLUME = {45},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {301--308},
      ISSN = {0024-6093},
   MRCLASS = {37P20 (11S20 37P05)},
  MRNUMBER = {3064415},
       DOI = {10.1112/blms/bds088},
       URL = {http://dx.doi.org/10.1112/blms/bds088},
}
@article {ingramhenon2011,
    AUTHOR = {Ingram, Patrick},
     TITLE = {Canonical heights for {H}\'{e}non maps},
   JOURNAL = {Proc. Lond. Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {108},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {780--808},
      ISSN = {0024-6115},
   MRCLASS = {37P30 (11G50 37P15)},
  MRNUMBER = {3180596},
       DOI = {10.1112/plms/pdt026},
       URL = {https://doi.org/10.1112/plms/pdt026},
}
@comment{UPDATE}
@misc {arxiv1310.4114,
    AUTHOR = {Ingram, Patrick},
    TITLE = {Rigidity and height bounds for certain post-critically
                  finite endomorphisms of projective space},
     YEAR = {2013},
     NOTE = {\url{arXiv:1310.4114}},
}
@comment{UPDATE}
@misc {arxiv2011.02968,
    AUTHOR = {Ingram, Patrick},
    TITLE = {Effective finiteness of solutions to certain differential and difference equations},
     YEAR = {2020},
     NOTE = {\url{arXiv:2011.02968}},
}
@comment{UPDATE}
@misc {arxiv2011.02975,
    AUTHOR = {Ingram, Patrick},
    TITLE = {Solutions to difference equations have few defects},
     YEAR = {2020},
     NOTE = {\url{arXiv:2011.02975}},
}
@comment{UPDATE}
@misc {arxiv2007.00567,
    AUTHOR = {Ingram, Patrick},
    TITLE = {Degree gaps for multipliers and the dynamical {A}ndre--{O}ort conjecture},
     YEAR = {2020},
     NOTE = {\url{arXiv:2007.00567}},
}
@comment{UPDATE}
@misc {arxiv2207.072067,
    AUTHOR = {Ingram, Patrick},
    TITLE = {Explicit canonical heights for divisors relative to endomorphisms of {$\mathbb{P}^N$}},
     YEAR = {2021},
     NOTE = {\url{arXiv:2207.07206}},
}
@comment{arxiv1408.5416}
@article {MR3436155,
    AUTHOR = {Ingram, Patrick},
     TITLE = {Variation of the canonical height for polynomials in several
              variables},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2015},
    NUMBER = {24},
     PAGES = {13545--13562},
      ISSN = {1073-7928},
   MRCLASS = {14G25 (14C20 14H25 37P30)},
  MRNUMBER = {3436155},
MRREVIEWER = {Nils R. Bruin},
       URL = {https://doi.org/10.1093/imrn/rnv121},
}
@comment{arxiv1411.1041}
@article {MR3885169,
    AUTHOR = {Ingram, Patrick},
     TITLE = {Canonical heights for correspondences},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {371},
      YEAR = {2019},
    NUMBER = {2},
     PAGES = {1003--1027},
      ISSN = {0002-9947},
   MRCLASS = {37P30 (37F05)},
  MRNUMBER = {3885169},
       DOI = {10.1090/tran/7288},
       URL = {https://doi.org/10.1090/tran/7288},
}
@comment{arxiv1411.6954}
@article {MR3664528,
    AUTHOR = {Ingram, Patrick},
     TITLE = {Critical dynamics of variable-separated affine
              correspondences},
   JOURNAL = {J. Lond. Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {95},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {1011--1034},
      ISSN = {0024-6107},
   MRCLASS = {37F05 (37P30)},
  MRNUMBER = {3664528},
MRREVIEWER = {Solomon Vishkautsan},
       DOI = {10.1112/jlms.12045},
       URL = {https://doi.org/10.1112/jlms.12045},
}
@comment{UPDATE}
@misc {arxiv1510.08807,
    AUTHOR = {Ingram, Patrick},
    TITLE = {Canonical heights and preperiodic points for
                  subhomogeneous families of polynomials}, 
     YEAR = {2015},
     NOTE = {\url{arXiv:1510.08807}},
}
@comment{arxiv1604.05197}
@article {MR3831927,
    AUTHOR = {Ingram, Patrick},
     TITLE = {{$p$}-adic uniformization and the action of {G}alois on
              certain affine correspondences},
   JOURNAL = {Canad. Math. Bull.},
  FJOURNAL = {Canadian Mathematical Bulletin. Bulletin Canadien de
              Math\'{e}matiques},
    VOLUME = {61},
      YEAR = {2018},
    NUMBER = {3},
     PAGES = {531--542},
      ISSN = {0008-4395},
   MRCLASS = {37P20 (11S20)},
  MRNUMBER = {3831927},
       DOI = {10.4153/CMB-2017-082-7},
       URL = {https://doi.org/10.4153/CMB-2017-082-7},
}
@comment{arxiv1610.07904}
@article {MR3799700,
    AUTHOR = {Ingram, Patrick},
     TITLE = {The critical height is a moduli height},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {167},
      YEAR = {2018},
    NUMBER = {7},
     PAGES = {1311--1346},
      ISSN = {0012-7094},
   MRCLASS = {37P30 (11G50)},
  MRNUMBER = {3799700},
MRREVIEWER = {Dragos Ghioca},
       DOI = {10.1215/00127094-2017-0053},
       URL = {https://doi.org/10.1215/00127094-2017-0053},
}
@comment{arxiv1706.05352}
@article {MR3936106,
    AUTHOR = {Ingram, Patrick},
     TITLE = {Critical orbits of polynomials with a periodic point of
              specified multiplier},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {291},
      YEAR = {2019},
    NUMBER = {3-4},
     PAGES = {1245--1262},
      ISSN = {0025-5874},
   MRCLASS = {37P30 (37P45)},
  MRNUMBER = {3936106},
       DOI = {10.1007/s00209-018-2118-x},
       URL = {https://doi.org/10.1007/s00209-018-2118-x},
}
@comment{UPDATE}
@misc {arxivarXiv:2006.12869,
    AUTHOR = {Ingram, Patrick},
    TITLE = {Minimally critical endomorphisms of $\mathbb{P}^N$},
     YEAR = {2020},
     NOTE = {\url{arXiv:2006.12869}},
}
@comment{UPDATE}
@misc {arxiv2006.15365,
    AUTHOR = {Ingram, Patrick},
    TITLE = {Minimally critical regular endomorphisms of $\mathbb{A}^N$},
     YEAR = {2020},
     NOTE = {\url{arXiv:2006.15365}},
}
@comment{UPDATE}
@misc {arxiv2104.12877,
    AUTHOR = {Ingram, Patrick},
    TITLE = {Variation of the canonical height in a family of polarized dynamical systems},
     YEAR = {2021},
     NOTE = {\url{arXiv:2104.12877}},
}
@comment{arXiv:0707.2505}
@article {MR2475968,
    AUTHOR = {Ingram, Patrick and Silverman, Joseph H.},
     TITLE = {Primitive divisors in arithmetic dynamics},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
              Society},
    VOLUME = {146},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {289--302},
      ISSN = {0305-0041},
     CODEN = {MPCPCO},
   MRCLASS = {11B37 (11A41 37Fxx)},
  MRNUMBER = {MR2475968},
}
@incollection {MR2867920,
    AUTHOR = {Ingram, Patrick and Silverman, Joseph H.},
     TITLE = {Uniform estimates for primitive divisors in elliptic
              divisibility sequences},
 BOOKTITLE = {Number theory, analysis and geometry},
     PAGES = {243--271},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2012},
   MRCLASS = {11G05 (11B37 14G25)},
  MRNUMBER = {2867920},
}
@misc {pcfinhighdim,
    AUTHOR = {Ingram, Patrick and Ramadas, Rohini and Silverman, Joseph H.},
     TITLE = {Post-critically finite maps in $\mathbb{P}^n$ for $n\ge2$ are sparse},
      NOTE = {preprint 2019, \url{arxiv.org/abs/1910.11290}},
}
@article {MR2076045,
    AUTHOR = {Ionascu, E. and Stanica, P.},
     TITLE = {Effective asymptotics for some nonlinear recurrences and
              almost doubly-exponential sequences},
   JOURNAL = {Acta Math. Univ. Comenian. (N.S.)},
  FJOURNAL = {Acta Mathematica Universitatis Comenianae. New Series},
    VOLUME = {73},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {75--87},
      ISSN = {0862-9544},
   MRCLASS = {11B37 (11B83 11K31)},
  MRNUMBER = {MR2076045 (2005f:11018)},
MRREVIEWER = {C{\'e}cile Dartyge},
}
@book {irelandrosen:gtm, 
    AUTHOR = {Ireland, Kenneth and Rosen, Michael},
     TITLE = {A {C}lassical {I}ntroduction to {M}odern {N}umber {T}heory},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {84},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1990},
     PAGES = {xiv+389},
      ISBN = {0-387-97329-X},
   MRCLASS = {11-01 (11-02)},
  MRNUMBER = {MR1070716 (92e:11001)},
MRREVIEWER = {Glenn Stevens},
}

@comment{--JJJ-- }

@comment{UPDATE}
@misc {arxiv1409.4808,
    AUTHOR = {Jacobs, Kenneth},
    TITLE = {An Equidistribution Result For Dynamical Systems on the
                  {B}erkovich Projective Line},
     YEAR = {2014},
     NOTE = {\url{arXiv:1409.4808}},
}
@comment{UPDATE}
@misc {arxiv1803.07460,
    AUTHOR = {Jacobs, Kenneth},
    TITLE = {Hyperbolic Equivariants of Rational Maps},
     YEAR = {2018},
     NOTE = {\url{arXiv:1803.07460}},
}
@article {MR3679789,
    AUTHOR = {Jacobs, Kenneth},
     TITLE = {Equidistribution of the crucial measures in non-{A}rchimedean
              dynamics},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {180},
      YEAR = {2017},
     PAGES = {86--138},
      ISSN = {0022-314X},
   MRCLASS = {37P50 (11S82 37P05 37P30)},
  MRNUMBER = {3679789},
       URL = {https://doi.org/10.1016/j.jnt.2017.02.018},
}
@comment{arxiv1510.02440}
@article {MR3937317,
    AUTHOR = {Jacobs, Kenneth},
     TITLE = {Lower bounds for non-{A}rchimedean {L}yapunov exponents},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {371},
      YEAR = {2019},
    NUMBER = {9},
     PAGES = {6025--6046},
      ISSN = {0002-9947},
   MRCLASS = {37P50 (11S82 37P05)},
  MRNUMBER = {3937317},
       DOI = {10.1090/tran/7344},
       URL = {https://doi.org/10.1090/tran/7344},
}
@article {MR3761441,
    AUTHOR = {Jacobs, Kenneth S.},
     TITLE = {Quantitative logarithmic equidistribution of the crucial
              measures},
   JOURNAL = {Res. Number Theory},
  FJOURNAL = {Research in Number Theory},
    VOLUME = {4},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {Art. 10, 32},
      ISSN = {2363-9555},
   MRCLASS = {37P05 (11S82)},
  MRNUMBER = {3761441},
       DOI = {10.1007/s40993-018-0094-1},
       URL = {https://doi.org/10.1007/s40993-018-0094-1},
}
@article {MR3982249,
    AUTHOR = {Jacobs, Kenneth and Williams, Phillip},
     TITLE = {Iteration and the minimal resultant},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {25},
      YEAR = {2019},
     PAGES = {451--466},
   MRCLASS = {37P05 (11S82 37P50)},
  MRNUMBER = {3982249},
MRREVIEWER = {Nicole R. Looper},
}
@book {MR734483,
    AUTHOR = {J{\"a}nich, Klaus},
     TITLE = {Topology},
    SERIES = {Undergraduate Texts in Mathematics},
      NOTE = {With a chapter by Theodor Br\"ocker,
              Translated from the German by Silvio Levy},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1984},
     PAGES = {ix+192},
      ISBN = {0-387-90892-7},
   MRCLASS = {54-01 (55-01 57-01)},
  MRNUMBER = {MR734483 (85a:54001)},
}
@comment{UPDATE}
@misc {arxiv1909.12187,
    AUTHOR = {Javanpeykar, Ariyan and Xie, Junyi},
    TITLE = {Finiteness properties of pseudo-hyperbolic varieties},
     YEAR = {2019},
     NOTE = {\url{arXiv:1909.12187}},
}
@article {MR2925477,
    AUTHOR = {Jenkins, Adrian and Spallone, Steven},
     TITLE = {Local analytic conjugacy of semi-hyperbolic mappings in two
              variables, in the non-{A}rchimedean setting},
   JOURNAL = {Internat. J. Math.},
  FJOURNAL = {International Journal of Mathematics},
    VOLUME = {23},
      YEAR = {2012},
    NUMBER = {6},
     PAGES = {1250059, 21},
      ISSN = {0129-167X},
   MRCLASS = {32P05 (37P20)},
  MRNUMBER = {2925477},
MRREVIEWER = {Karl-Olof Lindahl},
       DOI = {10.1142/S0129167X12500590},
       URL = {http://dx.doi.org/10.1142/S0129167X12500590},
}
@article {arXiv:0712.0963,
    AUTHOR = {Jenkins, Adrian and Spallone, Steven},
     TITLE = {A {$p$}-adic approach to local analytic dynamics: analytic
              conjugacy of analytic maps tangent to the identity},
   JOURNAL = {Ann. Fac. Sci. Toulouse Math. (6)},
  FJOURNAL = {Annales de la Facult\'e des Sciences de Toulouse.
              Math\'ematiques. S\'erie 6},
    VOLUME = {18},
      YEAR = {2009},
    NUMBER = {3},
     PAGES = {611--634},
      ISSN = {0240-2963},
   MRCLASS = {37P10 (30G06)},
  MRNUMBER = {2582444 (2011g:37251)},
MRREVIEWER = {Erlend Forn{\ae}ss Wold},
       URL = {http://afst.cedram.org/item?id=AFST_2009_6_18_3_611_0},
}

@comment{UPDATE}
@misc {arXiv:1011.2451,
    AUTHOR = {Jenkins, Adrian and Spallone, Steven},
    TITLE = {Lipeomorphic equivalence for $p$-adic analytic functions: 
            a comparison between complex and $p$-adic dynamics},
     YEAR = {2010},
     NOTE = {\url{arXiv:1011.2451}},
}
@article {MR3846809,
    AUTHOR = {Jeong, Sangtae},
     TITLE = {Bernoulli maps on {$\textbf{Z}_p$} in the expansions of van der
              {P}ut and {M}ahler},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {193},
      YEAR = {2018},
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}
@comment{UPDATE}
@misc {arxiv2105.06190,
    AUTHOR = {Jha, ZAbhishek},
    TITLE = {The density of numbers $n$ in a dynamical divisibility sequence having a fixed {G.C.D.} with their indices},
     YEAR = {2021},
     NOTE = {\url{arxiv:2105.06190}},
}
@comment{UPDATE}
@misc {arxiv2005.03628,
    AUTHOR = {Jia, Jia and Xie, Junyi and Zhang, De-Qi},
    TITLE = {Surjective endomorphisms of projective surfaces -- the existence of infinitely many dense orbits},
     YEAR = {2020},
     NOTE = {\url{arXiv:2005.03628}},
}
@comment{UPDATE}
@misc {arxiv2108.11595,
    AUTHOR = {Jia, Jia and Shibata, Takahiro and Zhang, De-Qi},
    TITLE = {Potential density of projective varieties having an int-amplified endomorphism},
     YEAR = {2021},
     NOTE = {\url{arXiv:2108.11595}},
}
@comment{UPDATE}
@misc {arxiv2104.05339,
    AUTHOR = {Jia, Jia and Shibata, Takahiro and Xie, Junyi and Zhang, De-Qi},  
    TITLE = {Endomorphisms of quasi-projective varieties -- {Z}ariski dense orbit and {K}awaguchi--{S}ilverman conjectures},
     YEAR = {2021},
     NOTE = {\url{arXiv:2104.05339}},
}
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     YEAR = {2005}
}

@article {jones:itgaltow,
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MRREVIEWER = {Thomas Ward},
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@article {MR2439638,
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@article {arXiv:1012.2857,
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@comment{arXiv:1402.6018}
@incollection {MR3220023,
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@comment{arXiv:1101.4339}
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@comment{arxiv1505.03559}
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@comment{UPDATE}
@misc {arxiv2205.11864,
    AUTHOR = {Jung, Barbara and von Pippich, Anna-Maria},
    TITLE = {The arithmetic volume of the moduli space of abelian surfaces},
     YEAR = {2022},
     NOTE = {\url{arXiv:2205.11864}},
}
@comment{UPDATE}
@misc {arxiv1903.05735,
    AUTHOR = {Jung, Myunghyun and Kim, Donggyun and Song, Kyunghwan},
    TITLE = {Dynamic Structures of $2$-adic {F}ibonacci Polynomials},
     YEAR = {2019},
     NOTE = {\url{arXiv:1903.05735}},
}
@comment{UPDATE}
@misc {arxiv1909.05605,
    AUTHOR = {Jung, Myunghyun and Kim, Donggyun},
    TITLE = {Dynamic Structures of Monomials on $p$-adic Integers for Small Primes $p$},
     YEAR = {2019},
     NOTE = {\url{arXiv:1909.05605}},
}
@article {MR4074552,
    AUTHOR = {Jung, Myunghyun and Kim, Donggyun},
     TITLE = {Dynamic structures of {$p$-adic monomials for small primes
              $p$}},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {211},
      YEAR = {2020},
     PAGES = {155--183},
      ISSN = {0022-314X},
   MRCLASS = {11S82 (37P35)},
  MRNUMBER = {4074552},
       DOI = {10.1016/j.jnt.2019.10.001},
       URL = {https://doi.org/10.1016/j.jnt.2019.10.001},
}


@comment{arxiv1410.3814}
@article {MR3885162,
    AUTHOR = {Juul, Jamie},
     TITLE = {Iterates of generic polynomials and generic rational
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   JOURNAL = {Trans. Amer. Math. Soc.},
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      ISSN = {0002-9947},
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  MRNUMBER = {3885162},
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       URL = {https://doi.org/10.1090/tran/7229},
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@comment{arxiv1603.06103}
@article {MR3820058,
    AUTHOR = {Juul, Jamie},
     TITLE = {Fixed point proportions for {G}alois groups of non-geometric
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  MRNUMBER = {3820058},
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       URL = {https://doi.org/10.4064/aa8535-2-2018},
}
@comment{UPDATE}
@misc {arxiv1706.07458,
    AUTHOR = {Juul, Jamie},
    TITLE = {The image size of iterated rational maps over finite fields},
     YEAR = {2017},
     NOTE = {\url{arXiv:1706.07458}},
}
@comment{arxiv1410.3378}
@article {MR3544625,
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              Tom J.},
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  MRNUMBER = {3544625},
MRREVIEWER = {Joseph H. Silverman},
       URL = {https://doi.org/10.1093/imrn/rnv273},
}
@comment{UPDATE}
@misc {arxiv1804.06053,
    AUTHOR = {Juul, Jamie and Krieger, Holly and Looper, Nicole and
                  Manes, Michelle and Thompson, Bianca and Walton,
                  Laura},
    TITLE = {Arboreal representations for rational maps with few critical points},
     YEAR = {2018},
     NOTE = {\url{arXiv:1804.06053}},
}

@comment{UPDATE}
@misc {arxiv2110.13890,
    AUTHOR = {Juul, Jamie and Krieger, Holly and Looper, Nicole and Mavraki, Niki Myrto},                 
    TITLE = {A dynamical {S}hafarevich theorem for endomorphisms of {$\mathbb{P}^N$}},
     YEAR = {2021},
     NOTE = {\url{arXiv:2110.13890}},
}



@comment{--KKK-- }

@comment{arxiv1802.09074}
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@comment{UPDATE}
@misc {arxiv2104.05118,
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     YEAR = {2021},
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@comment{UPDATE}
@misc {arxiv1510.04383,
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     NOTE = {\url{arXiv:1510.04383}},
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@comment{UPDATE}
@misc {arxiv1910.00904,
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     CODEN = {JRMAA8},
   MRCLASS = {14Gxx (11G50 37Fxx)},
  MRNUMBER = {MR2264317},
}

@article {kawrandom2005,
    AUTHOR = {Kawaguchi, Shu},
     TITLE = {Canonical heights for random iterations in certain varieties},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2007},
    NUMBER = {7},
     PAGES = {Art. ID rnm 023, 33},
      ISSN = {1073-7928},
   MRCLASS = {11G50 (14G25)},
  MRNUMBER = {MR2345343 (2009a:11136)},
MRREVIEWER = {Matthew H. Baker},
}

@article {kawtopent2005,
    AUTHOR = {Kawaguchi, Shu},
     TITLE = {Projective surface automorphisms of positive topological
              entropy from an arithmetic viewpoint},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {130},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {159--186},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {14G25 (11G35 14J50 37B40)},
  MRNUMBER = {MR2382145 (2008m:14042)},
MRREVIEWER = {Yuri Tschinkel},
}
@article {arxiv0909.3573,
    AUTHOR = {Kawaguchi, Shu},
     TITLE = {Local and global canonical height functions for affine space
              regular automorphisms},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {7},
      YEAR = {2013},
    NUMBER = {5},
     PAGES = {1225--1252},
      ISSN = {1937-0652},
   MRCLASS = {37P30 (11G50)},
  MRNUMBER = {3101078},
       DOI = {10.2140/ant.2013.7.1225},
       URL = {http://dx.doi.org/10.2140/ant.2013.7.1225},
}
@incollection {MR2868573,
    AUTHOR = {Kawaguchi, Shu},
     TITLE = {Introduction to algebraic and arithmetic dynamics---a survey},
 BOOKTITLE = {Algebraic number theory and related topics 2009},
    SERIES = {RIMS K\^oky\^uroku Bessatsu, B25},
     PAGES = {103--123},
 PUBLISHER = {Res. Inst. Math. Sci. (RIMS), Kyoto},
      YEAR = {2011},
   MRCLASS = {37Pxx (11G50 11S82 14G40)},
  MRNUMBER = {2868573},
}
@comment{UPDATE}
@misc {arxiv2103.02540,
    AUTHOR = {Kawaguchi, Shu and Mukai, Shigeru and Yoshikawa, Ken-Ichi},
    TITLE = {$J$-invariant and {B}orcherds phi-function},
     YEAR = {2021},
     NOTE = {\url{arXiv:2103.02540}},
}

@comment{UPDATE}
@misc {kawsilv:arithentropy,
    AUTHOR = {Kawaguchi, Shu and Silverman, Joseph H.},
     TITLE = {On Algebraic, Arithmetic, and Cohomological Entropies},
      YEAR = {2012},
      NOTE = {in preparation},
}
@comment{kawsilv:dfeqafPexamples}
@article {MR3189467,
    AUTHOR = {Kawaguchi, Shu and Silverman, Joseph H.},
     TITLE = {Examples of dynamical degree equals arithmetic degree},
   JOURNAL = {Michigan Math. J.},
  FJOURNAL = {Michigan Mathematical Journal},
    VOLUME = {63},
      YEAR = {2014},
    NUMBER = {1},
     PAGES = {41--63},
      ISSN = {0026-2285},
   MRCLASS = {Preliminary Data},
  MRNUMBER = {3189467},
       DOI = {10.1307/mmj/1395234358},
       URL = {http://dx.doi.org/10.1307/mmj/1395234358},
}
@comment{kawsilv:jordanblock}
@article {MR3456169,
    AUTHOR = {Kawaguchi, Shu and Silverman, Joseph H.},
     TITLE = {Dynamical canonical heights for {J}ordan blocks, arithmetic
              degrees of orbits, and nef canonical heights on abelian
              varieties},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {368},
      YEAR = {2016},
    NUMBER = {7},
     PAGES = {5009--5035},
      ISSN = {0002-9947},
   MRCLASS = {37P15 (11G10 11G50 37P30 37P55)},
  MRNUMBER = {3456169},
MRREVIEWER = {Dragos Ghioca},
       DOI = {10.1090/tran/6596},
       URL = {http://dx.doi.org/10.1090/tran/6596},
}
@article {MR4068299,
    AUTHOR = {Kawaguchi, Shu and Silverman, Joseph H.},
     TITLE = {Addendum to ``{D}ynamical canonical heights for {J}ordan
              blocks, arithmetic degrees of orbits, and nef canonical
              heights on abelian varieties"},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {373},
      YEAR = {2020},
    NUMBER = {3},
     PAGES = {2253},
      ISSN = {0002-9947},
   MRCLASS = {37P15 (11G10 11G50 37P30 37P55)},
  MRNUMBER = {4068299},
       DOI = {10.1090/tran/7905},
       URL = {https://doi.org/10.1090/tran/7905},
}
@comment{kawsilv:arithdegledyndeg}
@article {MR3483624,
    AUTHOR = {Kawaguchi, Shu and Silverman, Joseph H.},
     TITLE = {On the dynamical and arithmetic degrees of rational self-maps
              of algebraic varieties},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {713},
      YEAR = {2016},
     PAGES = {21--48},
      ISSN = {0075-4102},
   MRCLASS = {37P55 (37P30)},
  MRNUMBER = {3483624},
MRREVIEWER = {Yu Yasufuku},
       DOI = {10.1515/crelle-2014-0020},
       URL = {http://dx.doi.org/10.1515/crelle-2014-0020},
}
@article {MR4080251,
    AUTHOR = {Kawaguchi, Shu and Silverman, Joseph H.},
     TITLE = {Erratum to {O}n the dynamical and arithmetic degrees of
              rational self-maps of algebraic varieties ({J}. reine angew.
              {M}ath. 713 (2016), 21--48)},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {761},
      YEAR = {2020},
     PAGES = {291--292},
      ISSN = {0075-4102},
   MRCLASS = {37P55 (37P30)},
  MRNUMBER = {4080251},
       DOI = {10.1515/crelle-2019-0024},
       URL = {https://doi.org/10.1515/crelle-2019-0024},
}
@article {kawsilidht2006,
    AUTHOR = {Kawaguchi, Shu and Silverman, Joseph H.},
     TITLE = {Dynamics of projective morphisms having identical canonical
              heights},
   JOURNAL = {Proc. Lond. Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {95},
      YEAR = {2007},
    NUMBER = {2},
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      ISSN = {0024-6115},
   MRCLASS = {11G50 (14G40 37F50)},
  MRNUMBER = {MR2352570 (2008j:11076)},
MRREVIEWER = {Matthew H. Baker},
      NOTE = {Addendum: Proc. Lond. Math. Soc. (3) 97 (2008), 272},
}

@article {kawsilarithcompl2006,
    AUTHOR = {Kawaguchi, Shu and Silverman, Joseph H.},
     TITLE = {Canonical heights and the arithmetic complexity of morphisms
              on projective space},
   JOURNAL = {Pure Appl. Math. Q.},
  FJOURNAL = {Pure and Applied Mathematics Quarterly},
    VOLUME = {5},
      YEAR = {2009},
    NUMBER = {4, Special Issue: In honor of John Tate. Part 1},
     PAGES = {1201--1217},
      ISSN = {1558-8599},
   MRCLASS = {11G50 (14G40 37Pxx)},
  MRNUMBER = {MR2560315},
}

@misc {kawsilholdergreen2006,
    AUTHOR = {Kawaguchi, Shu and Silverman, Joseph H.},
     TITLE = {Nonarchimedean {G}reen functions and dynamics on projective
              space},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {262},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {173--197},
      ISSN = {0025-5874},
     CODEN = {MAZEAX},
   MRCLASS = {32Uxx (11G25 32Pxx 37F10 37F50)},
  MRNUMBER = {MR2491605},
}
@comment{UPDATE}
@misc {arxiv1312.1311,
    AUTHOR = {Kaszian Jonas and  Moree, Pieter and Shparlinski, Igor E.},
    TITLE = {Periodic Structure of the Exponential Pseudorandom Number
                  Generator},
     YEAR = {2013},
     NOTE = {\url{arXiv:1312.1311}},
}

@comment{UPDATE}
@misc {arxiv2012.11306,
    AUTHOR = {Kazalicki, Matija and Naskr{\c{e}}cki, Bartosz},
    TITLE = {Second moments and the bias conjecture for the family of cubic pencils},
     YEAR = {2020},
     NOTE = {\url{arXiv:2012.11306}},
}


@inproceedings{keen:juliasets, 
   AUTHOR = {Keen, Linda},
    TITLE = {Julia sets of rational maps},
BOOKTITLE = {Complex Dynamical Systems},
     YEAR = {1994},
    PAGES = {71--90},
PUBLISHER = {American Mathematical Society},
   SERIES = {Proceedings of Symposia in Applied Mathematics},
   VOLUME = {49},
     NOTE = {Cincinnati (1994)}
}

@comment{UPDATE}
@misc {arxiv2008.00433,
    AUTHOR = {Kerr, Bryce and Mello, Jorge and Shparlinski, Igor E.},
    TITLE = {On elements of large order of elliptic curves and
                  multiplicative dependent images of rational
                  functions over finite fields},
     YEAR = {2020},
     NOTE = {\url{arXiv:2008.00433}},
}

@article {arxiv0511204,
    AUTHOR = {Khamraev, Murod and Mukhamedov, Farrukh},
     TITLE = {On a class of rational {$p$}-adic dynamical systems},
   JOURNAL = {J. Math. Anal. Appl.},
  FJOURNAL = {Journal of Mathematical Analysis and Applications},
    VOLUME = {315},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {76--89},
      ISSN = {0022-247X},
     CODEN = {JMANAK},
   MRCLASS = {37F10 (11S99 37A25)},
  MRNUMBER = {MR2196531 (2006j:37051)},
MRREVIEWER = {Liang-Chung Hsia},
}
@article {MR3962277,
    AUTHOR = {Kharchenko, V. P. and Glazunov, N. M.},
     TITLE = {Formal and non-{A}rchimedean structures of dynamical systems
              on manifolds},
   JOURNAL = {Kibernet. Sistem. Anal.},
  FJOURNAL = {Natsional\cprime naya Akademiya Nauk Ukrainy. Institut Kibernetiki
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    VOLUME = {55},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {45--55},
      ISSN = {1019-5262},
   MRCLASS = {37P20 (93A10)},
  MRNUMBER = {3962277},
MRREVIEWER = {Vladimir S. Anashin},
}
@comment{Detailed analysis of dynamics of ax^2/(bx+c)}
@article {MR3658132,
    AUTHOR = {Khayutin, Ilya},
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  MRNUMBER = {3658132},
MRREVIEWER = {Thomas Ward},
       URL = {https://doi.org/10.1093/imrn/rnw099},
}
@article {MR1696062,
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      YEAR = {1998},
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  MRNUMBER = {MR1696062 (2000d:92022)},
MRREVIEWER = {Eugen Belokolos},
}
@book {MR1746953,
    AUTHOR = {Khrennikov, Andrei},
     TITLE = {Non-{A}rchimedean analysis: quantum paradoxes, dynamical
              systems and biological models},
    SERIES = {Mathematics and its Applications},
    VOLUME = {427},
 PUBLISHER = {Kluwer Academic Publishers},
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      YEAR = {1997},
     PAGES = {xviii+371},
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   MRCLASS = {81-02 (00A69 11S85 11Z05 46S10 81P05)},
  MRNUMBER = {MR1746953 (2001h:81004)},
MRREVIEWER = {Bing Hong Wang},
}

@article {MR1989827,
    AUTHOR = {Khrennikov, Andrei and Nilsson, Marcus},
     TITLE = {Behaviour of {H}ensel perturbations of {$p$}-adic monomial
              dynamical systems},
   JOURNAL = {Anal. Math.},
  FJOURNAL = {Analysis Mathematica},
    VOLUME = {29},
      YEAR = {2003},
    NUMBER = {2},
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      ISSN = {0133-3852},
     CODEN = {ANMADK},
   MRCLASS = {11S85 (12J25 37B99)},
  MRNUMBER = {MR1989827 (2004g:11110)},
MRREVIEWER = {Teturo Kamae},
}
@incollection {MR1977444,
    AUTHOR = {Khrennikov, Andrei and Nilsson, Marcus and Nyqvist, Robert},
     TITLE = {The asymptotic number of periodic points of discrete
              polynomial {$p$}-adic dynamical systems},
 BOOKTITLE = {Ultrametric functional analysis (Nijmegen, 2002)},
    SERIES = {Contemp. Math.},
    VOLUME = {319},
     PAGES = {159--166},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2003},
   MRCLASS = {11S20 (37E15 37E99)},
  MRNUMBER = {MR1977444 (2004b:11158)},
MRREVIEWER = {Liang-Chung Hsia},
}
@article {MR1913640,
    AUTHOR = {Khrennikov, Andrei},
     TITLE = {Small denominators in complex {$p$}-adic dynamics},
   JOURNAL = {Indag. Math. (N.S.)},
  FJOURNAL = {Koninklijke Nederlandse Akademie van Wetenschappen.
              Indagationes Mathematicae. New Series},
    VOLUME = {12},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {177--189},
      ISSN = {0019-3577},
   MRCLASS = {11S85 (37F10)},
  MRNUMBER = {MR1913640 (2003e:11128)},
MRREVIEWER = {Manfred Einsiedler},
}

@article{DDNS559, 
   author = {Khrennikov, Andrei},
    title = {{$p$}-Adic discrete dynamical systems and collective behaviour of
          information states in cognitive models},
  journal = {Discrete Dynamics in Nature and Society},
     year = {2000},
   volume = {5},
   number = {1},
    pages = {59-69}
}

@article {MR1858076,
    AUTHOR = {Khrennikov, Andrei and Nilsson, Marcus},
     TITLE = {On the number of cycles of {$p$}-adic dynamical systems},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {90},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {255--264},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11S85 (37F10)},
  MRNUMBER = {MR1858076 (2002g:11172)},
MRREVIEWER = {Liang-Chung Hsia},
}
@incollection {MR1924983,
    AUTHOR = {Khrennikov, Andrei and Lindahl, Karl-Olof and Gundlach,
              Matthias},
     TITLE = {Ergodicity in the {$p$}-adic framework},
 BOOKTITLE = {Operator {M}ethods in {O}rdinary and {P}artial {D}ifferential
              {E}quations (Stockholm, 2000)},
    SERIES = {Oper. Theory Adv. Appl.},
    VOLUME = {132},
     PAGES = {245--251},
 PUBLISHER = {Birkh\"auser},
   ADDRESS = {Basel},
      YEAR = {2002},
   MRCLASS = {37E99 (11S85 37A99)},
  MRNUMBER = {MR1924983 (2003g:37083)},
}
@incollection {MR1830516,
    AUTHOR = {Khrennikov, Andrei},
     TITLE = {Ergodic and non-ergodic behaviour for dynamical systems in
              rings of {$p$}-adic integers},
 BOOKTITLE = {Fourth Italian-Latin American Conference on Applied and
              Industrial Mathematics (Havana, 2001)},
     PAGES = {404--409},
 PUBLISHER = {Inst. Cybern. Math. Phys., Havana},
      YEAR = {2001},
   MRCLASS = {37A45 (11S80 37A05)},
  MRNUMBER = {MR1830516 (2002b:37008)},
MRREVIEWER = {Anatoly N. Kochubei},
}

@book {MR2105195,
    AUTHOR = {Khrennikov, Andrei and Nilson, Marcus},
     TITLE = {{$p$}-adic {D}eterministic and {R}andom {D}ynamics},
    SERIES = {Mathematics and {I}ts Applications},
    VOLUME = {574},
 PUBLISHER = {Kluwer Academic Publishers},
   ADDRESS = {Dordrecht},
      YEAR = {2004},
     PAGES = {xviii+270},
      ISBN = {1-4020-2659-5},
   MRCLASS = {37F99 (11S85 28C10 28D15 37H99 37N25 92B20)},
  MRNUMBER = {MR2105195},
}
@comment{UPDATE}
@misc {arxiv1303.6472,
    AUTHOR = {Khrennikovm Andrei and Yurova, Ekaterina},
    TITLE = {Criteria of ergodicity for $p$-adic dynamical systems in
                  terms of coordinate functions},
     YEAR = {2013},
     NOTE = {\url{arXiv:1303.6472}},
}
@article {MR2994369,
    AUTHOR = {Khrennikov, Andrei and Yurova, Ekaterina},
     TITLE = {Criteria of measure-preserving for {$p$}-adic dynamical
              systems in terms of the van der {P}ut basis},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {133},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {484--491},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {37P20 (11S82)},
  MRNUMBER = {2994369},
MRREVIEWER = {Jean-Yves Briend},
       DOI = {10.1016/j.jnt.2012.08.013},
       URL = {http://dx.doi.org/10.1016/j.jnt.2012.08.013},
}
@article {MR3353266,
    AUTHOR = {Kihel, Omar and Larone, Jesse},
     TITLE = {Prime rational functions},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {169},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {29--46},
      ISSN = {0065-1036},
   MRCLASS = {11C08 (12E05 26C15)},
  MRNUMBER = {3353266},
MRREVIEWER = {Joshua Harrington},
       DOI = {10.4064/aa169-1-2},
       URL = {http://dx.doi.org/10.4064/aa169-1-2},
}
@comment{UPDATE}
@misc {arxiv1702.00735,
    AUTHOR = {Kim, Dohyeong},
    TITLE = {Integral points on the complement of plane quartics},
     YEAR = {2017},
     NOTE = {\url{arXiv:1702.00735}},
}
@article {math.DS/0701899,
    AUTHOR = {Kingsbery, James and Levin, Alex and Preygel, Anatoly and
              Silva, Cesar E.},
     TITLE = {Measurable dynamics of maps on profinite groups},
   JOURNAL = {Indag. Math. (N.S.)},
  FJOURNAL = {Koninklijke Nederlandse Akademie van Wetenschappen.
              Indagationes Mathematicae. New Series},
    VOLUME = {18},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {561--581},
      ISSN = {0019-3577},
   MRCLASS = {37A15 (28D15)},
  MRNUMBER = {MR2424314},
MRREVIEWER = {Radhakrishnan Nair},
}
@article {MR2439398,
    AUTHOR = {Kingsbery, James and Levin, Alex and Preygel, Anatoly and
              Silva, Cesar E.},
     TITLE = {On measure-preserving {$C\sp 1$} transformations of
              compact-open subsets of non-{A}rchimedean local fields},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {361},
      YEAR = {2009},
    NUMBER = {1},
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      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {37P20 (11S85 37A05 37A25 37A45 37F10)},
  MRNUMBER = {MR2439398},
}
@article {MR2773138,
    AUTHOR = {Kingsbery, James and Levin, Alex and Preygel, Anatoly and
              Silva, Cesar E.},
     TITLE = {Dynamics of the {$p$}-adic shift and applications},
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  FJOURNAL = {Discrete and Continuous Dynamical Systems. Series A},
    VOLUME = {30},
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    NUMBER = {1},
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      ISSN = {1078-0947},
   MRCLASS = {37Pxx (11S85 37Axx)},
  MRNUMBER = {2773138},
       DOI = {10.3934/dcds.2011.30.209},
       URL = {http://dx.doi.org/10.3934/dcds.2011.30.209},
}
@article {MR1326795,
    AUTHOR = {Kisaka, Masashi},
     TITLE = {On some exceptional rational maps},
   JOURNAL = {Proc. Japan Acad. Ser. A Math. Sci.},
  FJOURNAL = {Japan Academy. Proceedings. Series A. Mathematical Sciences},
    VOLUME = {71},
      YEAR = {1995},
    NUMBER = {2},
     PAGES = {35--38},
      ISSN = {0386-2194},
     CODEN = {PJAADT},
   MRCLASS = {30D05 (58F23)},
  MRNUMBER = {MR1326795 (96a:30029)},
MRREVIEWER = {I. N. Baker},
}
@comment{gives conjugacy classes of maps for I.N. Baker's description
of rational maps lacking a complex periodic point of some order}
@article {kiwi2006,
    AUTHOR = {Kiwi, Jan},
     TITLE = {Puiseux series polynomial dynamics and iteration of complex cubic
                     polynomials},
   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier},
    VOLUME = {56},
      YEAR = {2006},
    NUMBER = {5},
     PAGES = {1337--1404},
}
@comment{Rivera-Letelier notes: Kiwi shows that there are no wandering
domains for polynomial maps of degree 3 in the field of Puiseaux
series (the main result of this paper shows a deep connection between
ultrametric and complex dynamics)}

@incollection {MR1928528,
    AUTHOR = {Kleinbock, Dmitry and Shah, Nimish and Starkov, Alexander},
     TITLE = {Dynamics of subgroup actions on homogeneous spaces of {L}ie
              groups and applications to number theory},
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      YEAR = {2002},
   MRCLASS = {22F30 (11E57 22E30 37A45 37C85)},
  MRNUMBER = {MR1928528 (2004b:22021)},
MRREVIEWER = {Mikhail S. Kulikov},
}

@book {MR1193029,
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 PUBLISHER = {Princeton University Press},
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   MRCLASS = {11G05 (11-01 11F11 14H52)},
  MRNUMBER = {MR1193029 (93j:11032)},
MRREVIEWER = {Joseph H. Silverman},
}

@article {MR402127,
    AUTHOR = {Kobayashi, Shoshichi and Ochiai, Takushiro},
     TITLE = {Meromorphic mappings onto compact complex spaces of general
              type},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {31},
      YEAR = {1975},
    NUMBER = {1},
     PAGES = {7--16},
      ISSN = {0020-9910},
   MRCLASS = {32H99 (32H25)},
  MRNUMBER = {402127},
MRREVIEWER = {Hirotaka Fujimoto},
       DOI = {10.1007/BF01389863},
       URL = {https://doi.org/10.1007/BF01389863},
}
	
@book {MR1216136,
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   MRCLASS = {11G05 (11F11 11F37 11G40 14H52)},
  MRNUMBER = {MR1216136 (94a:11078)},
}
@book {MR754003,
    AUTHOR = {Koblitz, Neal},
     TITLE = {{$p$}-adic {N}umbers, {$p$}-adic {A}nalysis, and
                  {Z}eta-{F}unctions},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {58},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1984},
     PAGES = {xii+150},
      ISBN = {0-387-96017-1},
   MRCLASS = {11Q25 (11S80)},
  MRNUMBER = {MR754003 (86c:11086)},
}
@article {MR3263519,
    AUTHOR = {Hubbard, John H. and Koch, Sarah},
     TITLE = {An analytic construction of the {D}eligne-{M}umford
              compactification of the moduli space of curves},
   JOURNAL = {J. Differential Geom.},
  FJOURNAL = {Journal of Differential Geometry},
    VOLUME = {98},
      YEAR = {2014},
    NUMBER = {2},
     PAGES = {261--313},
      ISSN = {0022-040X},
   MRCLASS = {32G15 (14H10)},
  MRNUMBER = {3263519},
       URL = {http://projecteuclid.org/euclid.jdg/1406552251},
}
@article {MR3107522,
    AUTHOR = {Koch, Sarah},
     TITLE = {Teichm\"uller theory and critically finite endomorphisms},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {248},
      YEAR = {2013},
     PAGES = {573--617},
      ISSN = {0001-8708},
   MRCLASS = {37F10},
  MRNUMBER = {3107522},
       DOI = {10.1016/j.aim.2013.08.019},
       URL = {http://dx.doi.org/10.1016/j.aim.2013.08.019},
}
@article {MR3119600,
    AUTHOR = {Buff, Xavier and Epstein, Adam L. and Koch, Sarah},
     TITLE = {B\"ottcher coordinates},
   JOURNAL = {Indiana Univ. Math. J.},
  FJOURNAL = {Indiana University Mathematics Journal},
    VOLUME = {61},
      YEAR = {2012},
    NUMBER = {5},
     PAGES = {1765--1799},
      ISSN = {0022-2518},
   MRCLASS = {32H50 (32B10 32M25 32U05 37F50)},
  MRNUMBER = {3119600},
MRREVIEWER = {Feng Rong},
       DOI = {10.1512/iumj.2012.61.4981},
       URL = {http://dx.doi.org/10.1512/iumj.2012.61.4981},
}
@article {MR3088270,
    AUTHOR = {Buff, Xavier and Epstein, Adam L. and Koch, Sarah and Meyer,
              Daniel and Pilgrim, Kevin and Rees, Mary and Lei, Tan},
     TITLE = {Questions about polynomial matings},
   JOURNAL = {Ann. Fac. Sci. Toulouse Math. (6)},
  FJOURNAL = {Annales de la Facult\'e des Sciences de Toulouse.
              Math\'ematiques. S\'erie 6},
    VOLUME = {21},
      YEAR = {2012},
    NUMBER = {5},
     PAGES = {1149--1176},
      ISSN = {0240-2963},
   MRCLASS = {37F10},
  MRNUMBER = {3088270},
       DOI = {10.5802/afst.1365},
       URL = {http://dx.doi.org/10.5802/afst.1365},
}
@article {MR3088265,
    AUTHOR = {Buff, Xavier and Epstein, Adam L. and Koch, Sarah},
     TITLE = {Twisted matings and equipotential gluings},
   JOURNAL = {Ann. Fac. Sci. Toulouse Math. (6)},
  FJOURNAL = {Annales de la Facult\'e des Sciences de Toulouse.
              Math\'ematiques. S\'erie 6},
    VOLUME = {21},
      YEAR = {2012},
    NUMBER = {5},
     PAGES = {995--1031},
      ISSN = {0240-2963},
   MRCLASS = {37F30 (32G05 32G15 37F10)},
  MRNUMBER = {3088265},
MRREVIEWER = {Athanase Papadopoulos},
       DOI = {10.5802/afst.1360},
       URL = {http://dx.doi.org/10.5802/afst.1360},
}
@incollection {MR2933889,
    AUTHOR = {Antol{\'{\i}}n-Camarena, Omar and Koch, Sarah},
     TITLE = {On a theorem of {K}as and {S}chlessinger},
 BOOKTITLE = {Quasiconformal mappings, {R}iemann surfaces, and
              {T}eichm\"uller spaces},
    SERIES = {Contemp. Math.},
    VOLUME = {575},
     PAGES = {13--22},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2012},
   MRCLASS = {32S30 (14B07 32C15)},
  MRNUMBER = {2933889},
MRREVIEWER = {Vasile Br{\^{\i}}nz{\u{a}}nescu},
       DOI = {10.1090/conm/575/11401},
       URL = {http://dx.doi.org/10.1090/conm/575/11401},
}
@incollection {MR2581826,
    AUTHOR = {Belk, James and Koch, Sarah},
     TITLE = {Iterated monodromy for a two-dimensional map},
 BOOKTITLE = {In the tradition of {A}hlfors-{B}ers. {V}},
    SERIES = {Contemp. Math.},
    VOLUME = {510},
     PAGES = {1--11},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2010},
   MRCLASS = {14D05 (37F30)},
  MRNUMBER = {2581826 (2011c:14019)},
MRREVIEWER = {Meirav Topol},
       DOI = {10.1090/conm/510/10013},
       URL = {http://dx.doi.org/10.1090/conm/510/10013},
}
@article {MR3425238,
    AUTHOR = {Konyagin, Sergei V. and Luca, Florian and Mans, Bernard and
              Mathieson, Luke and Sha, Min and Shparlinski, Igor E.},
     TITLE = {Functional graphs of polynomials over finite fields},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {116},
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   MRCLASS = {05E18 (05C20 05C85 11T06 11T24)},
  MRNUMBER = {3425238},
MRREVIEWER = {Nick Gill},
       DOI = {10.1016/j.jctb.2015.07.003},
       URL = {https://doi.org/10.1016/j.jctb.2015.07.003},
}
@comment{UPDATE}
@misc {arxiv1711.05335,
    AUTHOR = {Konyagin, S. V. and Makarychev, S. V. and Shparlinski,
                  I. E. and Vyugin, I. V.},
    TITLE = {On the new bound for the number of solutions of
                  polynomial equations in subgroups and the structure
                  of graphs of {M}arkoff triples},
     YEAR = {2017},
     NOTE = {\url{arXiv:1711.05335}},
}
@comment{UPDATE}
@misc {arxiv2005.05315,
    AUTHOR = {Konyagin, S. V.  and Shparlinski, I. E. and Vyugin,  I. V.},
    TITLE = {Polynomial Equations in Subgroups and Applications},
     YEAR = {2020},
     NOTE = {\url{arXiv:2005.05315}},
}
@article {MR4112680,
    AUTHOR = {Konyagin, Sergei V. and Makarychev, Sergey V. and Shparlinski,
              Igor E. and Vyugin, Ilya V.},
     TITLE = {On the structure of graphs of {M}arkoff triples},
   JOURNAL = {Q. J. Math.},
  FJOURNAL = {The Quarterly Journal of Mathematics},
    VOLUME = {71},
      YEAR = {2020},
    NUMBER = {2},
     PAGES = {637--648},
      ISSN = {0033-5606},
   MRCLASS = {11G25 (11D09 11J06)},
  MRNUMBER = {4112680},
MRREVIEWER = {Yann Bugeaud},
       DOI = {10.1093/qmathj/haz055},
       URL = {https://doi.org/10.1093/qmathj/haz055},
}
	
@comment{UPDATE}
@misc {arxiv1606.04368,
    AUTHOR = {Koll{\'a}r, J{\'a}nos},
    TITLE = {Severi--{B}rauer varieties; a geometric treatment},
     YEAR = {2016},
     NOTE = {\url{arXiv:1606.04368}},
}
@book {MR1658959,
    AUTHOR = {Koll{\'a}r, J{\'a}nos and Mori, Shigefumi},
     TITLE = {Birational {G}eometry of {A}lgebraic {V}arieties},
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    VOLUME = {134},
      NOTE = {With the collaboration of C. H. Clemens and A. Corti,
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   ADDRESS = {Cambridge},
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     PAGES = {viii+254},
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  MRNUMBER = {1658959 (2000b:14018)},
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       DOI = {10.1017/CBO9780511662560},
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}
@article {MR3015990,
    AUTHOR = {Kool, J.},
     TITLE = {Dynamics measured in a non-{A}rchimedean field},
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  FJOURNAL = {p-Adic Numbers, Ultrametric Analysis, and Applications},
    VOLUME = {5},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {1--13},
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   MRCLASS = {37P20 (37P05)},
  MRNUMBER = {3015990},
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       DOI = {10.1134/S2070046613010019},
       URL = {http://dx.doi.org/10.1134/S2070046613010019},
}
@article {arxiv1205.3694,
    AUTHOR = {Koymans, Peter},
     TITLE = {The generalized {C}atalan equation in positive characteristic},
   JOURNAL = {Int. J. Number Theory},
  FJOURNAL = {International Journal of Number Theory},
      YEAR = {2022},
       DOI = {10.1142/S179304212250018X},
      NOTE = {published online, 8 pages},
}
@incollection {arxiv0608105,
    AUTHOR = {Kra, Bryna},
     TITLE = {Ergodic methods in additive combinatorics},
 BOOKTITLE = {Additive combinatorics},
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      YEAR = {2007},
   MRCLASS = {37A30 (11B25 37A45 47A35)},
  MRNUMBER = {MR2359470 (2008k:37018)},
MRREVIEWER = {Tom Sanders},
}
@comment{Survey article based on four lectures}
@book {MR1710388,
    AUTHOR = {Krantz, Steven G.},
     TITLE = {A panorama of harmonic analysis},
    SERIES = {Carus Mathematical Monographs},
    VOLUME = {27},
 PUBLISHER = {Mathematical Association of America, Washington, DC},
      YEAR = {1999},
     PAGES = {xvi+357},
      ISBN = {0-88385-031-1},
   MRCLASS = {42-01},
  MRNUMBER = {1710388},
MRREVIEWER = {Javier Duoandikoetxea},
}
@comment {arXiv1203.2555}
@article {MR3142262,
    AUTHOR = {Krieger, Holly},
     TITLE = {Primitive prime divisors in the critical orbit of {$z^d+c$}},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2013},
    NUMBER = {23},
     PAGES = {5498--5525},
      ISSN = {1073-7928},
   MRCLASS = {11B83 (11A41 37F10 37P05)},
  MRNUMBER = {3142262},
MRREVIEWER = {P. Bundschuh},
       URL = {https://doi.org/10.1093/imrn/rns213},
}
@comment{arxiv1406.1990}
@article {MR3320871,
    AUTHOR = {Krieger, Holly and Levin, Aaron and Scherr, Zachary and
              Tucker, Thomas and Yasufuku, Yu and Zieve, Michael E.},
     TITLE = {Uniform boundedness of {$S$}-units in arithmetic dynamics},
   JOURNAL = {Pacific J. Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {274},
      YEAR = {2015},
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   MRCLASS = {37P05 (11G35 14G25 37P15)},
  MRNUMBER = {3320871},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.2140/pjm.2015.274.97},
       URL = {http://dx.doi.org/10.2140/pjm.2015.274.97},
}
@comment{arxiv1508.03830}
@article {MR3562026,
    AUTHOR = {Krumm, David},
     TITLE = {A local-global principle in the dynamics of quadratic
              polynomials},
   JOURNAL = {Int. J. Number Theory},
  FJOURNAL = {International Journal of Number Theory},
    VOLUME = {12},
      YEAR = {2016},
    NUMBER = {8},
     PAGES = {2265--2297},
      ISSN = {1793-0421},
   MRCLASS = {37P15 (11S20 20B35 37P05 37P20)},
  MRNUMBER = {3562026},
MRREVIEWER = {Rafe Jones},
       URL = {https://doi.org/10.1142/S1793042116501360},
}
@comment{MR3766922}
@article {arxiv1707.02501,
    AUTHOR = {Krumm, David},
     TITLE = {Galois groups in a family of dynatomic polynomials},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {187},
      YEAR = {2018},
     PAGES = {469--511},
      ISSN = {0022-314X},
   MRCLASS = {11R32 (11R09)},
  MRNUMBER = {3766922},
       DOI = {10.1016/j.jnt.2017.11.011},
       URL = {https://doi.org/10.1016/j.jnt.2017.11.011},
}
@comment{MR3951585}
@article {arxiv1805.11152,
    AUTHOR = {Krumm, David},
     TITLE = {A finiteness theorem for specializations of dynatomic
              polynomials},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {13},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {963--993},
      ISSN = {1937-0652},
   MRCLASS = {37P05 (11S15 37P35)},
  MRNUMBER = {3951585},
       DOI = {10.2140/ant.2019.13.963},
       URL = {https://doi.org/10.2140/ant.2019.13.963},
}

@article {MR0062973,
    AUTHOR = {Kruskal, Martin D.},
     TITLE = {The expected number of components under a random mapping
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   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {61},
      YEAR = {1954},
     PAGES = {392--397},
      ISSN = {0002-9890},
   MRCLASS = {60.0X},
  MRNUMBER = {0062973},
MRREVIEWER = {R. Fortet},
       URL = {https://doi.org/10.2307/2307900},
}
@article {MR3857595,
    AUTHOR = {K\"{u}\c{c}\"{u}ksakall\i , \"{O}mer},
     TITLE = {Value sets of bivariate folding polynomials over finite
              fields},
   JOURNAL = {Finite Fields Appl.},
  FJOURNAL = {Finite Fields and their Applications},
    VOLUME = {54},
      YEAR = {2018},
     PAGES = {253--272},
      ISSN = {1071-5797},
   MRCLASS = {11T06},
  MRNUMBER = {3857595},
       DOI = {10.1016/j.ffa.2018.05.008},
       URL = {https://doi.org/10.1016/j.ffa.2018.05.008},
}
@article {MR3787740,
    AUTHOR = {K\"{u}\c{c}\"{u}ksakall\i , \"{O}mer and \"{O}nsiper, Hur\c{s}it},
     TITLE = {Arithmetic exceptionality of generalized {L}att\`es maps},
   JOURNAL = {J. Math. Soc. Japan},
  FJOURNAL = {Journal of the Mathematical Society of Japan},
    VOLUME = {70},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {823--832},
      ISSN = {0025-5645},
   MRCLASS = {11G20 (14H52 20H15)},
  MRNUMBER = {3787740},
       DOI = {10.2969/jmsj/07027643},
       URL = {https://doi.org/10.2969/jmsj/07027643},
}
@article {MR3778551,
    AUTHOR = {K\"{u}\c{c}\"{u}ksakall\i , \"{O}mer},
     TITLE = {On the arithmetic exceptionality of polynomial mappings},
   JOURNAL = {Bull. Lond. Math. Soc.},
  FJOURNAL = {Bulletin of the London Mathematical Society},
    VOLUME = {50},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {143--147},
      ISSN = {0024-6093},
   MRCLASS = {11T06},
  MRNUMBER = {3778551},
MRREVIEWER = {Daniel Panario},
       DOI = {10.1112/blms.12129},
       URL = {https://doi.org/10.1112/blms.12129},
}
@article {MR3515828,
    AUTHOR = {K\"{u}\c{c}\"{u}ksakall\i , \"{O}mer},
     TITLE = {Bivariate polynomial mappings associated with simple complex
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   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {168},
      YEAR = {2016},
     PAGES = {433--451},
      ISSN = {0022-314X},
   MRCLASS = {11T06 (17B22)},
  MRNUMBER = {3515828},
MRREVIEWER = {Daniel Panario},
       DOI = {10.1016/j.jnt.2016.04.021},
       URL = {https://doi.org/10.1016/j.jnt.2016.04.021},
}
@article {MR3396383,
    AUTHOR = {K\"{u}\c{c}\"{u}ksakall\i , \"{O}mer},
     TITLE = {Value sets of bivariate {C}hebyshev maps over finite fields},
   JOURNAL = {Finite Fields Appl.},
  FJOURNAL = {Finite Fields and their Applications},
    VOLUME = {36},
      YEAR = {2015},
     PAGES = {189--202},
      ISSN = {1071-5797},
   MRCLASS = {11T06},
  MRNUMBER = {3396383},
MRREVIEWER = {Omran Ahmadi Darvishvand},
       DOI = {10.1016/j.ffa.2015.08.005},
       URL = {https://doi.org/10.1016/j.ffa.2015.08.005},
}
@article {MR3227347,
    AUTHOR = {K\"{u}\c{c}\"{u}ksakall\i , \"{O}mer},
     TITLE = {Value sets of {L}att\`es maps over finite fields},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {143},
      YEAR = {2014},
     PAGES = {262--278},
      ISSN = {0022-314X},
   MRCLASS = {11G20},
  MRNUMBER = {3227347},
MRREVIEWER = {Nurdag\"{u}l Anbar},
       DOI = {10.1016/j.jnt.2014.04.014},
       URL = {https://doi.org/10.1016/j.jnt.2014.04.014},
}
@comment{UPDATE}
@misc {arxiv2101.10272,
    AUTHOR = {K\"{u}hne, Lars},
    TITLE = {Equidistribution in Families of Abelian Varieties and Uniformity},
     YEAR = {2021},
     NOTE = {\url{arXiv:2101.10272}},
}
@article {MR1817250,
    AUTHOR = {Kulikov, V. S. and Kulikov, Vik. S.},
     TITLE = {Generic coverings of the plane with
              {$A$}-{$D$}-{$E$}-singularities},
   JOURNAL = {Izv. Ross. Akad. Nauk Ser. Mat.},
  FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Izvestiya. Seriya
              Matematicheskaya},
    VOLUME = {64},
      YEAR = {2000},
    NUMBER = {6},
     PAGES = {65--106},
      ISSN = {0373-2436},
   MRCLASS = {14J17 (14E22 14J29)},
  MRNUMBER = {1817250 (2002c:14058)},
MRREVIEWER = {Alexander Zvonkin},
       DOI = {10.1070/IM2000v064n06ABEH000312},
       URL = {http://dx.doi.org/10.1070/IM2000v064n06ABEH000312},
}
@comment{UPDATE}
@misc {arxiv1402.4464,
    AUTHOR = {Kurlberg, P{\"a}r and Luca, Florian and Shparlinski, Igor},
    TITLE = {On the Fixed Points of the Map $x \to x^x$ Modulo a Prime},
     YEAR = {2014},
     NOTE = {\url{arXiv:1402.4464}},
}

@comment{--LLL-- }

@incollection {lagarias:numbertheoryanddynamics,
    AUTHOR = {Lagarias, J. C.},
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@misc {arxiv0608208,
    AUTHOR = {Lagarias, J. C.},
    TITLE = {The $3x+1$ Problem: {A}n Annotated Bibliography, {I} \& {I}{I}},
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     NOTE = {\url{ArXiv:math.NT/0309224}, \url{ArXiv:math.NT/0608208}},
}

@article {lagariassloan2004,
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   MRCLASS = {11K31 (11B83)},
  MRNUMBER = {MR2065571 (2005c:11098)},
MRREVIEWER = {Thomas Ward},
}
@comment{UPDATE}
@misc {arxiv2206.04290,
    AUTHOR = {Laishram, Shanta and Sarma, Ritumoni and Sharma, Himanshu},
    TITLE = {Stability of Certain Higher Degree Polynomials},
     YEAR = {2022},
     NOTE = {\url{arXiv:2206.04290}},
}
@article {Landau35,
    AUTHOR = {Landau, Edmund},
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   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {1},
      YEAR = {1935},
     PAGES = {43--62},
}
@book{lang:numbertheory,
    AUTHOR = {Lang, Serge},
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    SERIES = {Graduate Texts in Mathematics},
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   EDITION = {Second},
 PUBLISHER = {Springer-Verlag},
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      YEAR = {1994},
     PAGES = {xiv+357},
      ISBN = {0-387-94225-4},
   MRCLASS = {11Rxx (11-01 11-02)},
  MRNUMBER = {MR1282723 (95f:11085)},
MRREVIEWER = {M. Ram Murty},
}

@book{lang:diophantinegeometry, 
    AUTHOR = {Lang, Serge},
     TITLE = {Fundamentals of {D}iophantine {G}eometry},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1983},
     PAGES = {xviii+370},
      ISBN = {0-387-90837-4},
   MRCLASS = {11-02 (11Dxx 11Gxx 14G25)},
  MRNUMBER = {MR715605 (85j:11005)},
MRREVIEWER = {Gerd Faltings},
}

@book{lang:algebra, 
    AUTHOR = {Lang, Serge},
     TITLE = {Algebra},
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    VOLUME = {211},
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@book {MR518817,
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@book {langalgabelianfncs,
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 PUBLISHER = {Springer-Verlag},
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@book {MR0214547,
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 PUBLISHER = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don
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@book {MR890960,
    AUTHOR = {Lang, Serge},
     TITLE = {Elliptic {F}unctions},
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 PUBLISHER = {Springer-Verlag},
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   MRCLASS = {11F03 (11G05 11G07 11G15 14G25)},
  MRNUMBER = {MR890960 (88c:11028)},
}

@article{lattes:iteration, 
   AUTHOR = {S. Latt\`es},
    TITLE = {Sur l'iteration des substitutions rationelles et les fonctions de {P}oincar{\'{e}}},
  JOURNAL = {Comptes Rendus Acad. Sci. Paris},
   VOLUME = {166},
     YEAR = {1918},
    PAGES = {26--28}
	}

@techreport{lauschleicher:irreducibility,
   AUTHOR = {Lau, E. and Schleicher, D.},
    TITLE = {Internal addresses in the {M}andelbrot set and 
                   irreducibility of polynomials},
    MONTH = {December},
     YEAR = {1994},
PUBLISHER = {SUNY StonyBrook},
   SERIES = {Institute for Mathematical Sciences Preprint},
   NUMBER = {1994/19}
	}


@article {MR1914256,
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     CODEN = {CMPMAF},
   MRCLASS = {11S15 (14L05 37F99)},
  MRNUMBER = {MR1914256 (2003f:11179)},
MRREVIEWER = {Jean-Pierre Wintenberger},
}
@book {MR2095471,
    AUTHOR = {Lazarsfeld, Robert},
     TITLE = {Positivity in algebraic geometry. {I}},
    SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A
              Series of Modern Surveys in Mathematics [Results in
              Mathematics and Related Areas. 3rd Series. A Series of Modern
              Surveys in Mathematics]},
    VOLUME = {48},
      NOTE = {Classical setting: line bundles and linear series},
 PUBLISHER = {Springer-Verlag},
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     PAGES = {xviii+387},
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   MRCLASS = {14-02 (14C20)},
  MRNUMBER = {2095471 (2005k:14001a)},
MRREVIEWER = {Mihnea Popa},
       DOI = {10.1007/978-3-642-18808-4},
       URL = {http://dx.doi.org/10.1007/978-3-642-18808-4},
}

@inproceedings{laurent:lehmer, 
   AUTHOR = {Laurent, M.},
    TITLE = {Minoration de la hauteur de {N}\'eron-{T}ate},
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     YEAR = {1983},
    PAGES = {137--151},
PUBLISHER = {Birkh\"auser},
   SERIES = {Progress in Mathematics},
     NOTE = {Paris 1981--1982}
}
@comment{UPDATE}
@misc {arxiv2112.12005,
    AUTHOR = {Le Boudec, Pierre and Mavraki, Niki Myrto},
    TITLE = {Arithmetic dynamics of random polynomials},
     YEAR = {2022},
     NOTE = {\url{arXiv:2112.12005}},
}
@book {MR2794839,
    AUTHOR = {Lee, Chong Gyu},
     TITLE = {Height estimates for rational maps},
      NOTE = {Thesis (Ph.D.)--Brown University},
 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {2010},
     PAGES = {72},
      ISBN = {978-1124-30208-9},
   MRCLASS = {Thesis},
  MRNUMBER = {2794839},
}
@article {arxiv0909.3107,
    AUTHOR = {Lee, Chong Gyu},
     TITLE = {An upper bound for the height for regular affine automorphisms
              of {$\mathbb{A}^n$}},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {355},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {1--16},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {14R10},
  MRNUMBER = {3004574},
       DOI = {10.1007/s00208-011-0775-8},
       URL = {http://dx.doi.org/10.1007/s00208-011-0775-8},
}
@comment{UPDATE}
@misc {arxiv1008.2394,
    AUTHOR = {Lee, ChongGyu},
    TITLE = {Height estimates for dominant endomorphisms on 
        projective varieties},
     YEAR = {2010},
     NOTE = {\url{arXiv:1008.2394}},
}
@article {MR3859838,
    AUTHOR = {Lee, Chong Gyu},
     TITLE = {Height inequality for rational maps and bounds for preperiodic
              points},
   JOURNAL = {Bull. Korean Math. Soc.},
  FJOURNAL = {Bulletin of the Korean Mathematical Society},
    VOLUME = {55},
      YEAR = {2018},
    NUMBER = {5},
     PAGES = {1317--1332},
      ISSN = {1015-8634},
   MRCLASS = {37P30 (11G50 14G50 32H50 32P05)},
  MRNUMBER = {3859838},
}
@article {arxiv1102.4860,
    AUTHOR = {Lee, Chong Gyu},
     TITLE = {Equidistribution of periodic points of some automorphisms on
              {$K3$} surfaces},
   JOURNAL = {Bull. Korean Math. Soc.},
  FJOURNAL = {Bulletin of the Korean Mathematical Society},
    VOLUME = {49},
      YEAR = {2012},
    NUMBER = {2},
     PAGES = {307--317},
      ISSN = {1015-8634},
   MRCLASS = {37Pxx (14J28 14J50)},
  MRNUMBER = {2934481},
       DOI = {10.4134/BKMS.2012.49.2.307},
       URL = {http://dx.doi.org/10.4134/BKMS.2012.49.2.307},
}


@article {MR2975153,
    AUTHOR = {Lee, Chong Gyu},
     TITLE = {The numerical equivalence relation for height functions and
              ampleness and nefness criteria for divisors},
   JOURNAL = {Bull. Lond. Math. Soc.},
  FJOURNAL = {Bulletin of the London Mathematical Society},
    VOLUME = {44},
      YEAR = {2012},
    NUMBER = {5},
     PAGES = {944--960},
      ISSN = {0024-6093},
   MRCLASS = {11G50 (14C20 14G25 37P30)},
  MRNUMBER = {2975153},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.1112/blms/bds023},
       URL = {http://dx.doi.org/10.1112/blms/bds023},
}
@article {MR2885064,
    AUTHOR = {Lee, Chong Gyu},
     TITLE = {Height bound and preperiodic points for jointly regular
              families of rational maps},
   JOURNAL = {J. Korean Math. Soc.},
  FJOURNAL = {Journal of the Korean Mathematical Society},
    VOLUME = {48},
      YEAR = {2011},
    NUMBER = {6},
     PAGES = {1171--1187},
      ISSN = {0304-9914},
     CODEN = {JKMSDG},
   MRCLASS = {37P30 (11G50 32H50 37P05)},
  MRNUMBER = {2885064},
MRREVIEWER = {Rafe Jones},
       DOI = {10.4134/JKMS.2011.48.6.1171},
       URL = {http://dx.doi.org/10.4134/JKMS.2011.48.6.1171},
}
@article {MR3127046,
    AUTHOR = {Lee, Chong Gyu},
     TITLE = {The equidistribution of small points for strongly regular
              pairs of polynomial maps},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {275},
      YEAR = {2013},
    NUMBER = {3-4},
     PAGES = {1047--1072},
      ISSN = {0025-5874},
   MRCLASS = {11G50 (37P05 37P30)},
  MRNUMBER = {3127046},
       DOI = {10.1007/s00209-013-1169-2},
       URL = {http://dx.doi.org/10.1007/s00209-013-1169-2},
}
@article {leejhshenonstability,
    AUTHOR = {Lee, Chong Gyu and Silverman, Joseph H.},
     TITLE = {G{IT} stability of {H}\'{e}non maps},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {148},
      YEAR = {2020},
    NUMBER = {10},
     PAGES = {4263--4272},
      ISSN = {0002-9939},
   MRCLASS = {37P45 (14D22 14L24 37P05)},
  MRNUMBER = {4135295},
       DOI = {10.1090/proc/15055},
       URL = {https://doi.org/10.1090/proc/15055},
}
@article {MR3313423,
    AUTHOR = {Lee, Chong Gyu and Ye, Hexi},
     TITLE = {Finiteness of commutable maps of bounded degree},
   JOURNAL = {Bull. Korean Math. Soc.},
  FJOURNAL = {Bulletin of the Korean Mathematical Society},
    VOLUME = {52},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {45--56},
      ISSN = {1015-8634},
   MRCLASS = {37P05 (37F10 37P35)},
  MRNUMBER = {3313423},
       DOI = {10.4134/BKMS.2015.52.1.045},
       URL = {http://dx.doi.org/10.4134/BKMS.2015.52.1.045},
}
@incollection {MR3509803,
    AUTHOR = {Lee, Junghun},
     TITLE = {An alternative proof of the non-{A}rchimedean {M}ontel theorem
              for polynomial dynamics},
 BOOKTITLE = {Advances in non-{A}rchimedean analysis},
    SERIES = {Contemp. Math.},
    VOLUME = {665},
     PAGES = {133--137},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2016},
   MRCLASS = {37P40 (11S82 26E30 37P05)},
  MRNUMBER = {3509803},
MRREVIEWER = {Solomon Vishkautsan},
       DOI = {10.1090/conm/665/13340},
       URL = {https://doi.org/10.1090/conm/665/13340},
}
@article {MR3482752,
    AUTHOR = {Lee, Junghun},
     TITLE = {An alternative proof of the non-{A}rchimedean {M}ontel theorem
              for rational dynamics},
   JOURNAL = {Proc. Japan Acad. Ser. A Math. Sci.},
  FJOURNAL = {Japan Academy. Proceedings. Series A. Mathematical Sciences},
    VOLUME = {92},
      YEAR = {2016},
    NUMBER = {4},
     PAGES = {56--58},
      ISSN = {0386-2194},
   MRCLASS = {37P40 (11S82)},
  MRNUMBER = {3482752},
MRREVIEWER = {Solomon Vishkautsan},
       DOI = {10.3792/pjaa.92.56},
       URL = {https://doi.org/10.3792/pjaa.92.56},
}
@article {MR3916844,
    AUTHOR = {Lee, Junghun},
     TITLE = {{$J$}-stability of expanding maps in non-{A}rchimedean
              dynamics},
   JOURNAL = {Ergodic Theory Dynam. Systems},
  FJOURNAL = {Ergodic Theory and Dynamical Systems},
    VOLUME = {39},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {1002--1019},
      ISSN = {0143-3857},
   MRCLASS = {37P05 (37F15)},
  MRNUMBER = {3916844},
       DOI = {10.1017/etds.2017.53},
       URL = {https://doi.org/10.1017/etds.2017.53},
}
@article {MR1503118,
    AUTHOR = {Lehmer, D. H.},
     TITLE = {Factorization of certain cyclotomic functions},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {34},
      YEAR = {1933},
    NUMBER = {3},
     PAGES = {461--479},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {Database Expansion Item},
  MRNUMBER = {MR1503118},
}
@article {MR682664,
    AUTHOR = {Lenstra, A. K. and Lenstra, Jr., H. W. and Lov\'{a}sz, L.},
     TITLE = {Factoring polynomials with rational coefficients},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {261},
      YEAR = {1982},
    NUMBER = {4},
     PAGES = {515--534},
      ISSN = {0025-5831},
   MRCLASS = {12-04 (12A20 68C20 68C25)},
  MRNUMBER = {682664},
MRREVIEWER = {Daniel Lazard},
       DOI = {10.1007/BF01457454},
       URL = {https://doi.org/10.1007/BF01457454},
}
@article {MR4040853,
    AUTHOR = {Lerner, Emil},
     TITLE = {The uniform distribution of sequences generated by iterated
              polynomials},
   JOURNAL = {p-Adic Numbers Ultrametric Anal. Appl.},
  FJOURNAL = {p-Adic Numbers, Ultrametric Analysis, and Applications},
    VOLUME = {11},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {280--298},
      ISSN = {2070-0466},
   MRCLASS = {11K41 (11K45 11S82 37P05)},
  MRNUMBER = {4040853},
       DOI = {10.1134/S2070046619040034},
       URL = {https://doi.org/10.1134/S2070046619040034},
}
@comment{UPDATE}
@misc {arxiv1609.06391,
    AUTHOR = {Lesieutre, John},
    TITLE = {A projective variety with discrete, non-finitely generated automorphism group},
     YEAR = {2016},
     NOTE = {\url{arXiv:1609.06391}},
}
@comment{arxiv1604.08216}
@article {MR3904796,
    AUTHOR = {Lesieutre, John and Litt, Daniel},
     TITLE = {Dynamical {M}ordell-{L}ang and automorphisms of blow-ups},
   JOURNAL = {Algebr. Geom.},
  FJOURNAL = {Algebraic Geometry},
    VOLUME = {6},
      YEAR = {2019},
    NUMBER = {1},
     PAGES = {1--25},
      ISSN = {2214-2584},
   MRCLASS = {37P55 (14E07)},
  MRNUMBER = {3904796},
}

@comment{arxiv1802.07388}
@article {MR4259157,
    AUTHOR = {Lesieutre, John and Satriano, Matthew},
     TITLE = {Canonical heights on hyper-{K}\"{a}hler varieties and the
              {K}awaguchi-{S}ilverman conjecture},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2021},
    NUMBER = {10},
     PAGES = {7677--7714},
      ISSN = {1073-7928},
   MRCLASS = {37F80 (14G40 14J42 32Q25 37C35 37P05 37P35)},
  MRNUMBER = {4259157},
       DOI = {10.1093/imrn/rnz067},
       URL = {https://doi.org/10.1093/imrn/rnz067},
}
		
@comment{arxiv1809.00047}
@article {MR4157475,
    AUTHOR = {Lesieutre, John and Satriano, Matthew},
     TITLE = {A rational map with infinitely many points of distinct
              arithmetic degrees},
   JOURNAL = {Ergodic Theory Dynam. Systems},
  FJOURNAL = {Ergodic Theory and Dynamical Systems},
    VOLUME = {40},
      YEAR = {2020},
    NUMBER = {11},
     PAGES = {3051--3055},
      ISSN = {0143-3857},
   MRCLASS = {37P55 (14E07)},
  MRNUMBER = {4157475},
MRREVIEWER = {Sheng Meng},
       DOI = {10.1017/etds.2019.30},
       URL = {https://doi.org/10.1017/etds.2019.30},
}

@comment{UPDATE}
@misc {arxiv1604.00920,
    AUTHOR = {Levin, Aaron and Yasufuku, Yu },
    TITLE = {Integral points and orbits of endomorphisms on the projective plane},
     YEAR = {2016},
     NOTE = {\url{arXiv:1604.00920}},
}
@article {arxiv1109.6076,
    AUTHOR = {Levin, Aaron},
     TITLE = {Rational preimages in families of dynamical systems},
   JOURNAL = {Monatsh. Math.},
  FJOURNAL = {Monatshefte f\"ur Mathematik},
    VOLUME = {168},
      YEAR = {2012},
    NUMBER = {3-4},
     PAGES = {473--501},
      ISSN = {0026-9255},
     CODEN = {MNMTA2},
   MRCLASS = {37P15 (14G25 37P05)},
  MRNUMBER = {2993960},
MRREVIEWER = {Thomas Ward},
       DOI = {10.1007/s00605-012-0426-5},
       URL = {http://dx.doi.org/10.1007/s00605-012-0426-5},
}
@article {MR2506328,
    AUTHOR = {Levin, Genadi},
     TITLE = {Multipliers of periodic orbits of quadratic polynomials and
              the parameter plane},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {170},
      YEAR = {2009},
     PAGES = {285--315},
      ISSN = {0021-2172},
     CODEN = {ISJMAP},
   MRCLASS = {37F10 (30D05 30F45)},
  MRNUMBER = {MR2506328},
       DOI = {10.1007/s11856-009-0030-0},
       URL = {http://dx.doi.org/10.1007/s11856-009-0030-0},
}
@article {arxiv0809.0379,
    AUTHOR = {Levin, Genadi},
     TITLE = {Multipliers of periodic orbits in spaces of rational maps},
   JOURNAL = {Ergodic Theory Dynam. Systems},
  FJOURNAL = {Ergodic Theory and Dynamical Systems},
    VOLUME = {31},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {197--243},
      ISSN = {0143-3857},
   MRCLASS = {37F10 (37C25)},
  MRNUMBER = {2755929 (2012a:37095)},
MRREVIEWER = {Peter Ha{\"{\i}}ssinsky},
       DOI = {10.1017/S0143385709001059},
       URL = {http://dx.doi.org/10.1017/S0143385709001059},
}
@COMMENT{Defines operator T_f for a rational map f that
takes a function psi and gives a new function T_f(psi). Paper
proves an interesting identity, which author notes is then formally
true for maps over any characteristic 0 field. Question: How about
characteristic p?}

@article {MR1376996,
    AUTHOR = {Levin, G. and Przytycki, F.},
     TITLE = {When do two rational functions have the same {J}ulia set?},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {125},
      YEAR = {1997},
    NUMBER = {7},
     PAGES = {2179--2190},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {58F23 (30D05)},
  MRNUMBER = {MR1376996 (97i:58149)},
MRREVIEWER = {Walter Bergweiler},
}
@comment{MR4043216}
@incollection {arxiv1702.02582,
    AUTHOR = {Levin, Genadi and Shen, Weixiao and van Strien, Sebastian},
     TITLE = {Transversality for critical relations of families of rational
              maps: an elementary proof},
 BOOKTITLE = {New trends in one-dimensional dynamics},
    SERIES = {Springer Proc. Math. Stat.},
    VOLUME = {285},
     PAGES = {201--220},
 PUBLISHER = {Springer, Cham},
      YEAR = {[2019] \copyright 2019},
   MRCLASS = {37F45 (14E05 58K05)},
  MRNUMBER = {4043216},
       DOI = {10.1007/978-3-030-16833-9_11},
       URL = {https://doi.org/10.1007/978-3-030-16833-9_11},
}

@article {MR3007156,
    AUTHOR = {Levy, Alon},
     TITLE = {The semistable reduction problem for the space of morphisms on
              {$\mathbb{P}^n$}},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {6},
      YEAR = {2012},
    NUMBER = {7},
     PAGES = {1483--1501},
      ISSN = {1937-0652},
   MRCLASS = {14L24 (37P45 37P55)},
  MRNUMBER = {3007156},
MRREVIEWER = {Michael Louis Tepper},
       DOI = {10.2140/ant.2012.6.1483},
       URL = {https://doi.org/10.2140/ant.2012.6.1483},
}
@misc {arxiv1304.2834,
    AUTHOR = {Levy, Alon},
    TITLE = {The {McMullen} Map in Positive Characteristic},
     YEAR = {2013},
     NOTE = {\url{arXiv:1304.2834}},
}
@misc {arxiv1511.00793,
    AUTHOR = {Levy, Alon},
    TITLE = {Isolated Periodic Points in Several Nonarchimedean Variables},
     YEAR = {2015},
     NOTE = {\url{arXiv:1511.00793}},
}

@comment{arxiv0903.1318}
@article {MR2741188,
    AUTHOR = {Levy, Alon},
     TITLE = {The space of morphisms on projective space},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {146},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {13--31},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {37P45 (14E08)},
  MRNUMBER = {2741188},
       DOI = {10.4064/aa146-1-2},
       URL = {http://dx.doi.org/10.4064/aa146-1-2},
}
@article {MR3223364,
    AUTHOR = {Levy, Alon and Manes, Michelle and Thompson, Bianca},
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}
@article{lewis:invariantset, 
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     YEAR = {1972},
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@article {li:isogenies,
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  MRNUMBER = {MR1432775 (98a:11164)},
MRREVIEWER = {Kenneth Kramer},
}


@article {li:commutingpowerseries,
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@article {MR4064545,
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@comment{UPDATE}
@misc {arxiv2001.09721,
    AUTHOR = {Li, Ray and Shparlinski, Igor E.},
    TITLE = {Effective bounds on multiplicatively dependent orbits of integer polynomials modulo {$S$}-integers},
     YEAR = {2020},
     NOTE = {\url{arXiv:2001.09721}},
}

@comment{UPDATE}
@misc {arxiv2208.02616,
    AUTHOR = {Li, Sichen},
    TITLE = {Zariski orbit dense conjecture on birational automorphisms of projective threefolds},
     YEAR = {2022},
     NOTE = {\url{arXiv:2208.02616}},
}

@comment{UPDATE}
@misc {arxiv2209.06815,
    AUTHOR = {Li, Sichen},
    TITLE = {{K}awaguchi--{S}ilverman conjecture on birational automorphisms of projective threefolds},
     YEAR = {2022},
     NOTE = {\url{arXiv:2209.06815}},
}

@comment{UPDATE}
@misc {arxiv1810.10583,
    AUTHOR = {Liang, Ke and Rouse, Jeremy},
    TITLE = {The density of odd order reductions for elliptic curves with a rational point of order 2},
     YEAR = {2018},
     NOTE = {\url{arXiv:1810.10583}},
}
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@comment{arxiv1704.02661}
@article {MR4027555,
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@comment{UPDATE}
@misc {arxiv1205.2020,
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    TITLE = {Canonical Height Functions For Monomial Maps},
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     NOTE = {\url{arXiv:1205.2020}},
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@comment{UPDATE}
@misc {arxiv1403.3976,
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     YEAR = {2014},
     NOTE = {\url{arXiv:1403.3976}},
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@comment{UPDATE}
@misc {arxiv1803.05862,
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@comment{arxiv1311.4478}
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@comment{UPDATE}
@comment{Dynamical analogues? If not on P^1, then on P^n? Can do for dynatomic extension, or arboreal extension.}
@misc {arxiv2108.04270,
    AUTHOR = {Lombardo, Davide},
    TITLE = {Non-isogenous abelian varieties sharing the same division fields},
     YEAR = {2021},
     NOTE = {\url{arXiv:2108.04270}},
}
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MRREVIEWER = {Henry C. Pinkham},
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}
@comment{UPDATE}
@misc {arxiv2106.13003,
    AUTHOR = {Looper, Nicole R.},
    TITLE = {A {B}ogomolov property for the canonical height of maps with superattracting periodic points},
     YEAR = {2021},
     NOTE = {\url{arXiv:2106.13003}},
}
@article {arxiv1609.03398,
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     TITLE = {Dynamical {G}alois groups of trinomials and {O}doni's
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   JOURNAL = {Bull. Lond. Math. Soc.},
  FJOURNAL = {Bulletin of the London Mathematical Society},
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   MRCLASS = {37P15 (11R32 14G40 37P05)},
  MRNUMBER = {3937588},
MRREVIEWER = {Rafe Jones},
       DOI = {10.1112/blms.12227},
       URL = {https://doi.org/10.1112/blms.12227},
}
@comment{UPDATE}
@misc {arxiv2105.05240,
    AUTHOR = {Looper, Nicole},
    TITLE = {The Uniform Boundedness and Dynamical {L}ang Conjectures for polynomials},
     YEAR = {2021},
     NOTE = {\url{arXiv:2105.05240}},
}

@comment{arxiv1709.08121}
@article {MR3953120,
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   JOURNAL = {Math. Ann.},
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MRREVIEWER = {Dragos Ghioca},
       DOI = {10.1007/s00208-018-1735-3},
       URL = {https://doi.org/10.1007/s00208-018-1735-3},
}
@comment{UPDATE}
@misc {arxiv1711.01507,
    AUTHOR = {Looper, Nicole R.},
    TITLE = {The $abc$-conjecture implies uniform bounds on dynamical {Z}sigmondy sets},
     YEAR = {2017},
     NOTE = {\url{arXiv:1711.01507}},
}
@comment{arxiv1901.04385}
@article {MR4270662,
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@comment{UPDATE}
@misc {arxiv2108.09577,
    AUTHOR = {Looper, Nicole R. and Silverman, Joseph H.},
    TITLE = {A {L}ehmer-type height lower bound for abelian surfaces over function fields},
     YEAR = {2021},
     NOTE = {\url{arXiv:2108.09577}},
}
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@UNPUBLISHED{lubinunpub96,
  AUTHOR = {Lubin, Jonathan},
 TITLE   = {Seminar on $p$-adic time in nonarchimedean dynamical systems},
 NOTE    = {Seminar at {Brown} {University}},
 YEAR    = {prepared April 25, 1996}
}

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@book {MR1978431,
    AUTHOR = {Lubotzky, Alexander and Segal, Dan},
     TITLE = {Subgroup growth},
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 PUBLISHER = {Birkh\"auser Verlag, Basel},
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     PAGES = {xxii+453},
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   MRCLASS = {20E07 (20E18 20E26 20F69)},
  MRNUMBER = {1978431},
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       URL = {http://dx.doi.org/10.1007/978-3-0348-8965-0},
}
@comment{UPDATE}
@misc {arxiv1610.08109,
    AUTHOR = {Luca, F. and Ward, T.},
    TITLE = {An elliptic sequence is not a sampled linear recurrence sequence},
     YEAR = {2016},
     NOTE = {to appear in \emph{New York J. Math.}, \url{arXiv:1610.08109}},
}
@comment{Section 15.10 gives five proofs of the formula for the number of subgroups of Z^N of index n}
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@comment{arxiv1801.01440}
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@comment{--MMM-- }
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@article {MR1323985,
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@comment{UPDATE}
@misc {arxiv1411.6786,
    AUTHOR = {Maculan, Marco},
    TITLE = {Height on {GIT} quotients and {K}empf--{N}ess theory},
     YEAR = {2014},
     NOTE = {\url{arXiv:1411.6786}},
}
@article {MR3722572,
    AUTHOR = {Maculan, Marco},
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    NUMBER = {152},
      YEAR = {2017},
     PAGES = {149},
      ISSN = {0249-633X},
      ISBN = {978-2-85629-865-7},
   MRCLASS = {14L24 (11K60 14G40)},
  MRNUMBER = {3722572},
MRREVIEWER = {Ariyan Javanpeykar},
       DOI = {10.24033/msmf.460},
       URL = {https://doi.org/10.24033/msmf.460},
}
@article {MR1836434,
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@article {Mahler35,
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@article {MR3906564,
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@article {MR3015991,
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}
@article {MR732343,
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     TITLE = {On the dynamics of rational maps},
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@phdthesis{manesthesis, 
    AUTHOR = {Manes, Michelle},
     TITLE = {Arithmetic Dynamics and Moduli Spaces of Rational Maps},
   SCHOOL = {Brown University},
     YEAR = {2007},
}

@article {MR2407816,
    AUTHOR = {Manes, Michelle},
     TITLE = {{$\mathbb{Q}$}-rational cycles for degree-2 rational maps having
              an automorphism},
   JOURNAL = {Proc. Lond. Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {96},
      YEAR = {2008},
    NUMBER = {3},
     PAGES = {669--696},
      ISSN = {0024-6115},
   MRCLASS = {14G25 (11G99)},
  MRNUMBER = {MR2407816 (2009a:14029)},
MRREVIEWER = {Dipendra Prasad},
}

@article {MR2524186,
    AUTHOR = {Manes, Michelle},
     TITLE = {Moduli spaces for families of rational maps on {$\mathbb{P}^1$}},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {129},
      YEAR = {2009},
    NUMBER = {7},
     PAGES = {1623--1663},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {14D20 (11C08 11F03 11G99)},
  MRNUMBER = {MR2524186},
       DOI = {10.1016/j.jnt.2009.02.010},
       URL = {http://dx.doi.org/10.1016/j.jnt.2009.02.010},
}
@comment{MR4045425}
@article {arxiv1607.05772,
    AUTHOR = {Manes, Michelle and Silverman, Joseph H.},
     TITLE = {A classification of degree 2 semi-stable rational maps
                  {$\mathbb{P}^2\to\mathbb{P}^2$} with large finite
                  dynamical autormorphism group},
   JOURNAL = {Ann. Fac. Sci. Toulouse Math. (6)},
  FJOURNAL = {Annales de la Facult\'{e} des Sciences de Toulouse. Math\'{e}matiques.
              S\'{e}rie 6},
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      YEAR = {2019},
    NUMBER = {4},
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      ISSN = {0240-2963},
   MRCLASS = {37P45 (14E05 37P05)},
  MRNUMBER = {4045425},
       DOI = {10.5802/afst.1614},
       URL = {https://doi.org/10.5802/afst.1614},
}

@comment{arxiv1301.6158}
@article {MR3921872,
    AUTHOR = {Manes, Michelle and Thompson, Bianca},
     TITLE = {Periodic points in towers of finite fields for polynomials
              associated to algebraic groups},
   JOURNAL = {Rocky Mountain J. Math.},
  FJOURNAL = {The Rocky Mountain Journal of Mathematics},
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      YEAR = {2019},
    NUMBER = {1},
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      ISSN = {0035-7596},
   MRCLASS = {37P25 (11T06 37P05)},
  MRNUMBER = {3921872},
       DOI = {10.1216/rmj-2019-49-1-171},
       URL = {https://doi.org/10.1216/rmj-2019-49-1-171},
}
@article {manesyasu2011,
    AUTHOR = {Manes, Michelle and Yasufuku, Yu},
     TITLE = {Explicit descriptions of quadratic maps on $\mathbb{P}^1$},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {148},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {257--267},
}
@comment{UPDATE}
@misc {arxiv1908.10459,
    AUTHOR = {Manes, Michelle and Melamed, Gabrielle and Tobin, Bella},
    TITLE = {Dessins d'Enfants for Single-Cycle {B}elyi Maps},
     YEAR = {2019},
     NOTE = {\url{arXiv:1908.10459}},
}

@article {doi:10.1080/10586458.2017.1391725,
    AUTHOR = {Mans, Bernard and Sha, Min and Shparlinski, Igor E. and Sutantyo, Daniel},
     TITLE = {On Functional Graphs of Quadratic Polynomials},
   JOURNAL = {Exp. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {0},
      YEAR = {2017},
    NUMBER = {0},
     PAGES = {1--9},
       URL = {https://doi.org/10.1080/10586458.2017.1391725},
}
@phdthesis{marcellothesis, 
    AUTHOR = {Marcello, Sandra},
     TITLE = {Sur la dynamique arithm\'etique des automorphismes affines},
   SCHOOL = {Universit\'e Paris 7},
     YEAR = {2000},
}

@article {marcello:CR2000,
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     TITLE = {Sur les propri\'et\'es arithm\'etiques des it\'er\'es
              d'auto\-mor\-phismes r\'eguliers},
   JOURNAL = {C.~R.~Acad. Sci. Paris S\'er. I Math.},
  FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
              Math\'ematique},
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      YEAR = {2000},
    NUMBER = {1},
     PAGES = {11--16},
      ISSN = {0764-4442},
     CODEN = {CASMEI},
   MRCLASS = {11G50},
  MRNUMBER = {2001d:11072},
}

@article {MR1988948,
    AUTHOR = {Marcello, Sandra},
     TITLE = {Sur la dynamique arithm\'etique des automorphismes de l'espace
              affine},
   JOURNAL = {Bull. Soc. Math. France},
  FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France},
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    NUMBER = {2},
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   MRCLASS = {11G50 (32M17 37F10)},
  MRNUMBER = {MR1988948 (2004d:11053)},
MRREVIEWER = {Yuri Tschinkel},
}

@misc {arxiv0310434,
    AUTHOR = {Marcello, Sandra},
    TITLE = {G\'eom\'etrie, points rationnels et it\'er\'es 
                   des automorphismes de l'espace affine},
     YEAR = {2003},
     NOTE = {\url{ArXiv:math.NT/0310434}},
}

@misc {arxiv0310454,
    AUTHOR = {Marcello, Sandra},
    TITLE = {Sur des invariants g\'eom\'etriques associ\'es
                   aux automorphismes du plan affine},
     YEAR = {2003},
     NOTE = {\url{ArXiv:math.AG/0310454}},
}

@misc {arxiv0310417,
    AUTHOR = {Marcello, Sandra},
    TITLE = {Sur la dynamique p-adique arithm\'etique des 
                 automorphismes de l'espace affine},
     YEAR = {2003},
     NOTE = {\url{ArXiv:math.NT/0310417}},
}
@comment{the preceding three arxiv articles by Marcello are unlikely to ever be published}
@article {MR3030517,
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MRREVIEWER = {Yves Aubry},
       URL = {https://doi.org/10.1016/j.jalgebra.2013.01.035},
}

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  MRNUMBER = {1510073},
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}

@comment{UPDATE}
@misc {arxiv1505.02983,
    AUTHOR = {Martins, Rodrigo and Panario, Daniel },
    TITLE = {On the Heuristic of Approximating Polynomials over Finite
                  Fields by Random Mappings},
     YEAR = {2015},
     NOTE = {\url{arXiv:1505.02983}},
}

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@article {arxiv0705.2182,
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@article {MR0094360,
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@article {arxiv1606.00598,
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   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
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@comment{UPDATE}
@misc {htsclosedsubschemes2020,
    AUTHOR = {Matsuzawa, Yohsuke},
    TITLE = {Height functions associated with closed subschemes},
     YEAR = {2020},
     NOTE = {\url{arXiv:2008.08153}},
}
@comment{UPDATE}
@misc {arXiv2012.04693,
    AUTHOR = {Matsuzawa, Yohsuke},
    TITLE = {Vojta's conjecture, heights associated with subschemes, and primitive prime divisors in arithmetic dynamics},
     YEAR = {2020},
     NOTE = {\url{arXiv:2012.04693}},
}
@comment{arXiv:2008.08149}
@article {MR4247874,
    AUTHOR = {Matsuzawa, Yohsuke and Silverman, Joseph H.},
     TITLE = {The distribution relation and inverse function theorem in
              arithmetic geometry},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {226},
      YEAR = {2021},
     PAGES = {307--357},
      ISSN = {0022-314X},
   MRCLASS = {11G50 (14G40 37P30 47J07 58C15)},
  MRNUMBER = {4247874},
       DOI = {10.1016/j.jnt.2021.03.016},
       URL = {https://doi.org/10.1016/j.jnt.2021.03.016},
}
@article {arxiv1902.06072,
    AUTHOR = {Matsuzawa, Yohsuke},
     TITLE = {Kawaguchi-{S}ilverman conjecture for endomorphisms on several
              classes of varieties},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {366},
      YEAR = {2020},
     PAGES = {107086},
      ISSN = {0001-8708},
   MRCLASS = {37P05 (14E30 14G40 14J45 14M25 20G30)},
  MRNUMBER = {4070310},
       DOI = {10.1016/j.aim.2020.107086},
       URL = {https://doi.org/10.1016/j.aim.2020.107086},
}
@comment{UPDATE}
@misc {arxiv2005.08093,
    AUTHOR = {Matsuzawa, Yohsuke},
    TITLE = {Growth of local height functions along orbits of self-morphisms on projective varieties},
     YEAR = {2020},
     NOTE = {\url{arXiv:2005.08093}}
}
@comment{arxiv1802.03173}
@article {MR4092861,
    AUTHOR = {Matsuzawa, Yohsuke and Sano, Kaoru},
     TITLE = {Arithmetic and dynamical degrees of self-morphisms of
              semi-abelian varieties},
   JOURNAL = {Ergodic Theory Dynam. Systems},
  FJOURNAL = {Ergodic Theory and Dynamical Systems},
    VOLUME = {40},
      YEAR = {2020},
    NUMBER = {6},
     PAGES = {1655--1672},
      ISSN = {0143-3857},
   MRCLASS = {37P30 (11G50 14K05 37P55)},
  MRNUMBER = {4092861},
       DOI = {10.1017/etds.2018.117},
       URL = {https://doi.org/10.1017/etds.2018.117},
}
@comment{UPDATE}
@misc {arxiv2002.10976,
    AUTHOR = {Matsuzawa, Yohsuke and Meng, Sheng and Shibata, Takahiro and Zhang, De-Qi},
    TITLE = {Non-density of points of small arithmetic degrees},
     YEAR = {2020},
     NOTE = {\url{arXiv:2002.10976}},
}
@comment{UPDATE}
@misc {arxiv2005.13368,
    AUTHOR = {Matsuzawa, Yohsuke and Meng, Sheng and Shibata, Takahiro and Zhang, De-Qi and Zhong, Guolei},
    TITLE = {Invariant subvarieties with small dynamical degree},
     YEAR = {2020},
     NOTE = {\url{arXiv:2005.13368}},
}
@comment{MR3871505}
@article {arxiv1701.04369,
    AUTHOR = {Matsuzawa, Yohsuke and Sano, Kaoru and Shibata, Takahiro},
     TITLE = {Arithmetic degrees and dynamical degrees of endomorphisms on
              surfaces},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {12},
      YEAR = {2018},
    NUMBER = {7},
     PAGES = {1635--1657},
      ISSN = {1937-0652},
   MRCLASS = {14G05 (11G35 11G50 14E05 37P05 37P15 37P30)},
  MRNUMBER = {3871505},
       DOI = {10.2140/ant.2018.12.1635},
       URL = {https://doi.org/10.2140/ant.2018.12.1635},
}
@comment{MR3856845}
@article {arxiv1701.08937,
    AUTHOR = {Matsuzawa, Yohsuke and Sano, Kaoru and Shibata, Takahiro},
     TITLE = {Arithmetic degrees for dynamical systems over function fields
              of characteristic zero},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {290},
      YEAR = {2018},
    NUMBER = {3-4},
     PAGES = {1063--1083},
      ISSN = {0025-5874},
   MRCLASS = {37P15 (14E05)},
  MRNUMBER = {3856845},
MRREVIEWER = {Dragos Ghioca},
       DOI = {10.1007/s00209-018-2053-x},
       URL = {https://doi.org/10.1007/s00209-018-2053-x},
}
@comment{UPDATE}
@misc{YohsukeShou2019,
 AUTHOR = {Matsuzawa, Yohsuke and Yoshikawa, Shou},
  TITLE = {Kawaguchi--{S}ilverman Conjecture For Endomorphisms On
                  Rationally Connected Varieties Admitting An
                  Int-Amplified Endomorphism},
     YEAR = {2019},
     NOTE = {\url{arXiv:1908.11537}},
}
@comment{UPDATE}
@misc{MatsuzawaGrowthLocalHt2020,
 AUTHOR = {Matsuzawa, Yohsuke},
  TITLE = {GROWTH OF LOCAL HEIGHT FUNCTIONS ALONG ORBITS OF SELF-MORPHISMS ON PROJECTIVE VARIETIES},
     YEAR = {2020},
     NOTE = {\url{arXiv:xxx}},
}
@comment{UPDATE}
@misc {arxiv1502.04660, 
    AUTHOR = {Mavraki, Niki Myrto and Ye, Hexi},
    TITLE = {Quasi-adelic measures and equidistribution on {$\mathbb{P}^1$}},
     YEAR = {2017},
     NOTE = {\url{arXiv:1502.04660}},
}
@comment{UPDATE}
@misc {arxiv2201.10455, 
    AUTHOR = {Mavraki, Niki Myrto and Schmidt, Harry},
    TITLE = {On the dynamical {B}ogomolov conjecture for families of split rational maps},
     YEAR = {2022},
     NOTE = {\url{arXiv:2201.10455}},
}
@comment{UPDATE}
@misc {arxiv2208.01597, 
    AUTHOR = {Mavraki, Niki Myrto and Schmidt, Harry and Wilms, Robert},
    TITLE = {Height coincidences in products of the projective line},
     YEAR = {2022},
     NOTE = {\url{arXiv:2208.01597}},
}
@article {mazur:uniformbound,
    AUTHOR = {Mazur, B.},
     TITLE = {Modular curves and the {E}isenstein ideal},
   JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
  FJOURNAL = {Institut des Hautes \'Etudes Scientifiques. Publications
              Math\'ematiques},
    NUMBER = {47},
      YEAR = {1977},
     PAGES = {33--186 (1978)},
      ISSN = {0073-8301},
     CODEN = {PMIHA6},
   MRCLASS = {14G25 (10D05)},
  MRNUMBER = {MR488287 (80c:14015)},
MRREVIEWER = {M. Ohta},
}

@incollection {mcmillan:integmap,
    AUTHOR = {McMillan, E. M.},
     TITLE = {A problem in the stability of periodic systems},
 BOOKTITLE = {Topics in Modern Physics: A Tribute to E. U. Condon},
     PAGES = {219--244},
 PUBLISHER = {Colorado Assoc. Univ. Press},
   ADDRESS = {Boulder, CO},
      YEAR = {1971},
}
@comment{The first integrable map of the plane was introduced by
E. M. McMillan \ref[in Topics in modern physics: a tribute to
E. U. Condon, 219--244, Colorado Assoc. Univ. Press, Boulder, CO,
1971], and contained 6 arbitrary parameters. This map was generalized
to an 18-parameter map, that is now commonly called the QRT map.}

@article{mcmullen:rootfinding, 
    AUTHOR = {McMullen, Curtis T.},
     TITLE = {Families of rational maps and iterative root-finding
              algorithms},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {125},
      YEAR = {1987},
    NUMBER = {3},
     PAGES = {467--493},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {58F08 (58C15 65H05)},
  MRNUMBER = {MR890160 (88i:58082)},
MRREVIEWER = {Michael Hurley},
}
@book {MR1312365,
    AUTHOR = {McMullen, Curtis T.},
     TITLE = {Complex dynamics and renormalization},
    SERIES = {Annals of Mathematics Studies},
    VOLUME = {135},
 PUBLISHER = {Princeton University Press},
   ADDRESS = {Princeton, NJ},
      YEAR = {1994},
     PAGES = {x+214},
      ISBN = {0-691-02982-2; 0-691-02981-4},
   MRCLASS = {58F23 (30D05)},
  MRNUMBER = {1312365 (96b:58097)},
MRREVIEWER = {Gregery T. Buzzard},
}

@article {MR1896103,
    AUTHOR = {McMullen, Curtis T.},
     TITLE = {Dynamics on {$K3$} surfaces: {S}alem numbers and {S}iegel
              disks},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {545},
      YEAR = {2002},
     PAGES = {201--233},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {37F25 (11F06 32H50 32J15 32Q15 37C40)},
  MRNUMBER = {MR1896103 (2003a:37057)},
MRREVIEWER = {Serge Cantat},
}
@article {MR1713286,
    AUTHOR = {McMullen, Curtis T.},
     TITLE = {From dynamics on surfaces to rational points on curves},
   JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
  FJOURNAL = {American Mathematical Society. Bulletin. New Series},
    VOLUME = {37},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {119--140},
      ISSN = {0273-0979},
     CODEN = {BAMOAD},
   MRCLASS = {11G30 (32G15 37E30 57M60)},
  MRNUMBER = {MR1713286 (2000j:11093)},
MRREVIEWER = {Joseph H. Silverman},
}

@article {MR1620850,
    AUTHOR = {McMullen, Curtis T. and Sullivan, Dennis P.},
     TITLE = {Quasiconformal homeomorphisms and dynamics. {III}. {T}he
              {T}eichm\"uller space of a holomorphic dynamical system},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {135},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {351--395},
      ISSN = {0001-8708},
     CODEN = {ADMTA4},
   MRCLASS = {58F23 (30C62 30D05 30F60)},
  MRNUMBER = {MR1620850 (99e:58145)},
MRREVIEWER = {Athanase Papadopoulos},
}

@comment{UPDATE}
@misc {arxiv0901.2352,
    AUTHOR = {Medvedev, Alice and Scanlon, Thomas},
    TITLE = {Polynomial dynamics},
     YEAR = {2009},
     NOTE = {\url{arXiv:0901.2352}},
}
@comment{UPDATE}
@misc {arxiv2203.05083,
    AUTHOR = {Medvedev, Alice and Nguyen, Khoa Dang and Scanlon, Thomas},
    TITLE = {Skew-invariant curves and the algebraic independence of {M}ahler functions},
     YEAR = {2022},
     NOTE = {\url{arXiv:2203.05083}},
}
@article {MR3126567,
    AUTHOR = {Medvedev, Alice and Scanlon, Thomas},
     TITLE = {Invariant varieties for polynomial dynamical systems},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {179},
      YEAR = {2014},
    NUMBER = {1},
     PAGES = {81--177},
      ISSN = {0003-486X},
   MRCLASS = {37F10 (14C99 14H99)},
  MRNUMBER = {3126567},
       DOI = {10.4007/annals.2014.179.1.2},
       URL = {https://doi.org/10.4007/annals.2014.179.1.2},
}
@comment{UPDATE}
@misc {arxiv1910.08539,
    AUTHOR = {Mello, Jorge},
    TITLE = {On semigroup orbits of polynomials and multiplicative orders},
     YEAR = {2019},
     NOTE = {\url{arXiv:1910.08539}},
}
@comment{UPDATE}
@misc {arxiv1910.07637,
    AUTHOR = {Mello, Jorge},
    TITLE = {On semigroup orbits of polynomials in subgroups},
     YEAR = {2019},
     NOTE = {\url{arXiv:1910.07637}},
}
@comment{UPDATE}
@misc {arxiv1707.07782,
    AUTHOR = {Mello, Jorge},
    TITLE = {A bound for the sum of heights on iterates in terms of a dynamical degree},
     YEAR = {2017},
     NOTE = {\url{arXiv:1707.07782}},
}
@comment{arxiv1707.09464}
@article {MR4009574,
    AUTHOR = {Mello, Jorge},
     TITLE = {On variation of dynamical canonical heights for semigroups of
              morphisms},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {224},
      YEAR = {2020},
    NUMBER = {3},
     PAGES = {1195--1204},
      ISSN = {0022-4049},
   MRCLASS = {37P55 (11G50)},
  MRNUMBER = {4009574},
MRREVIEWER = {Nicole R. Looper},
       DOI = {10.1016/j.jpaa.2019.07.013},
       URL = {https://doi.org/10.1016/j.jpaa.2019.07.013},
}
@comment{arxiv1708.00951}
@article {MR3996355,
    AUTHOR = {Mello, Jorge},
     TITLE = {Canonical heights and monomial maps: on effective lower bounds
              for points with dense orbit},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {205},
      YEAR = {2019},
     PAGES = {321--339},
      ISSN = {0022-314X},
   MRCLASS = {11G50 (14G40 37P35)},
  MRNUMBER = {3996355},
MRREVIEWER = {Valerio Talamanca},
       DOI = {10.1016/j.jnt.2019.05.013},
       URL = {https://doi.org/10.1016/j.jnt.2019.05.013},
}

@comment{UPDATE}
@misc {arxiv1907.03934,
    AUTHOR = {Mello, Jorge},
    TITLE = {On intersections of polynomial semigroups orbits with plane lines},
     YEAR = {2019},
     NOTE = {\url{arXiv:1907.03934}},
}
@comment{UPDATE}
@misc {arxiv2009.00947,
    AUTHOR = {Mello, Jorge},
    TITLE = {Cyclotomic preperiodic points for morphisms in affine spaces and preperiodic points with bounded house and height},
     YEAR = {2020},
     NOTE = {\url{arXiv:2009.00947}},
}
@comment{UPDATE}
@misc {arxiv2012.01844,
    AUTHOR = {Mello, Jorge},
    TITLE = {On effective $\epsilon$-integrality in orbits of rational maps over function fields and multiplicative dependence},
     YEAR = {2020},
     NOTE = {\url{arXiv:2012.01844}},
}
@article {MR4023669,
    AUTHOR = {Mello, Jorge},
     TITLE = {On quantitative estimates for quasiintegral points in orbits
              of semigroups of rational maps},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {25},
      YEAR = {2019},
     PAGES = {1091--1111},
   MRCLASS = {37P15 (11G50 14E05)},
  MRNUMBER = {4023669},
MRREVIEWER = {Simone Ugolini},
}
@article {MR3673068,
    AUTHOR = {Memi\'c, Nacima},
     TITLE = {Ergodic polynomials on 2-adic spheres},
   JOURNAL = {Bull. Pol. Acad. Sci. Math.},
  FJOURNAL = {Bulletin of the Polish Academy of Sciences. Mathematics},
    VOLUME = {65},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {35--44},
      ISSN = {0239-7269},
   MRCLASS = {37P20 (11S82)},
  MRNUMBER = {3673068},
       URL = {https://doi.org/10.4064/ba8099-1-2017},
}
@incollection {MR3174936,
    AUTHOR = {Mendes, S{\'e}rgio},
     TITLE = {On the dynamics of a cubic {$p$}-adic polynomial},
 BOOKTITLE = {Nonlinear maps and their applications},
    SERIES = {Springer Proc. Math. Stat.},
    VOLUME = {57},
     PAGES = {141--148},
 PUBLISHER = {Springer, New York},
      YEAR = {2014},
   MRCLASS = {37P05 (11S82)},
  MRNUMBER = {3174936},
MRREVIEWER = {Thomas Ward},
       DOI = {10.1007/978-1-4614-9161-3_14},
       URL = {http://dx.doi.org/10.1007/978-1-4614-9161-3_14},
}
@comment{UPDATE}
@misc {arxiv1908.01605,
    AUTHOR = {Meng, Sheng and Zhang, De-Qi},
    TITLE = {Kawaguchi--{S}ilverman conjecture for surjective endomorphisms},
     YEAR = {2019},
     NOTE = {\url{arXiv:1908.01605}},
}
@misc {arxiv2009.01089,
    AUTHOR = {Merai, Lazlo and Shparlinski, Igor E.},
    TITLE = {On the Dynamical System Generated by the {M\"obius} transformation at Prime Times},
     YEAR = {2020},
     NOTE = {\url{arXiv:2009.01089}},
}
@article{merel:uniformbound, 
    AUTHOR = {Merel, Lo{\"{\i}}c},
     TITLE = {Bornes pour la torsion des courbes elliptiques sur les corps
              de nombres},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {124},
      YEAR = {1996},
    NUMBER = {1-3},
     PAGES = {437--449},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11G05 (11L05)},
  MRNUMBER = {MR1369424 (96i:11057)},
MRREVIEWER = {Henri Darmon},
}
@comment{arxiv1904.12621}
@article {MR4043665,
    AUTHOR = {M\'{e}rai, L\'{a}szl\'{o} and Shparlinski, Igor E.},
     TITLE = {Unlikely intersections over finite fields: polynomial orbits
              in small subgroups},
   JOURNAL = {Discrete Contin. Dyn. Syst.},
  FJOURNAL = {Discrete and Continuous Dynamical Systems. Series A},
    VOLUME = {40},
      YEAR = {2020},
    NUMBER = {2},
     PAGES = {1065--1073},
      ISSN = {1078-0947},
   MRCLASS = {11D79 (11T06 37P05 37P25)},
  MRNUMBER = {4043665},
       DOI = {10.3934/dcds.2020070},
       URL = {https://doi.org/10.3934/dcds.2020070},
}
@comment{UPDATE}
@misc {arxiv1905.11657,
    AUTHOR = {M{\'e}rai, L{\'a}zl{\'o} and Ostafe, Alina and Shparlinski, Igor},
    TITLE = {Dynamical irreducibility of polynomials in reduction modulo primes},
     YEAR = {2019},
     NOTE = {\url{arXiv:1905.11657}},
}
@article {MR785222,
    AUTHOR = {M{\'e}rindol, Jean-Yves},
     TITLE = {Propri\'et\'es \'el\'ementaires des surfaces {$K3$}},
      NOTE = {Geometry of $K3$ surfaces: moduli and periods (Palaiseau,
              1981/1982)},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {126},
      YEAR = {1985},
     PAGES = {45--57},
      ISSN = {0303-1179},
   MRCLASS = {32J15},
  MRNUMBER = {MR785222},
}
@article {MR250909,
    AUTHOR = {Metropolis, N. and Stein, M. L. and Stein, P. R.},
     TITLE = {Permanents of cyclic {$(0,\,1)$} matrices},
   JOURNAL = {J. Combinatorial Theory},
  FJOURNAL = {Journal of Combinatorial Theory},
    VOLUME = {7},
      YEAR = {1969},
     PAGES = {291--321},
      ISSN = {0021-9800},
   MRCLASS = {05.25 (15.00)},
  MRNUMBER = {250909},
MRREVIEWER = {B. R. Heap},
}
@book {MR1777382,
    AUTHOR = {Meyer, Carl},
     TITLE = {Matrix analysis and applied linear algebra},
      NOTE = {With 1 CD-ROM (Windows, Macintosh and UNIX) and a solutions
              manual (iv+171 pp.)},
 PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)},
   ADDRESS = {Philadelphia, PA},
      YEAR = {2000},
     PAGES = {xii+718},
      ISBN = {0-89871-454-0},
   MRCLASS = {15-01},
  MRNUMBER = {1777382},
       DOI = {10.1137/1.9780898719512},
       URL = {http://dx.doi.org/10.1137/1.9780898719512},
}
@article {MR3709645,
    AUTHOR = {Miasnikov, Nikita and Stout, Brian and Williams, Phillip},
     TITLE = {Automorphism loci for the moduli space of rational maps},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {180},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {267--296},
      ISSN = {0065-1036},
   MRCLASS = {37P45 (14D22 14E05)},
  MRNUMBER = {3709645},
       URL = {https://doi.org/10.4064/aa8548-6-2017},
}
@article {MR0384708,
    AUTHOR = {Mignotte, M.},
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   JOURNAL = {J. Austral. Math. Soc.},
  FJOURNAL = {Australian Mathematical Society. Journal. Series A. Pure
              Mathematics and Statistics},
    VOLUME = {20},
      YEAR = {1975},
    NUMBER = {2},
     PAGES = {242--244},
      ISSN = {0263-6115},
   MRCLASS = {10F05},
  MRNUMBER = {0384708 (52 \#5581)},
MRREVIEWER = {Joseph Arkin},
}
@incollection {MR2457739,
    AUTHOR = {Mikhalkin, Grigory and Zharkov, Ilia},
     TITLE = {Tropical curves, their {J}acobians and theta functions},
 BOOKTITLE = {Curves and abelian varieties},
    SERIES = {Contemp. Math.},
    VOLUME = {465},
     PAGES = {203--230},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2008},
   MRCLASS = {14T05 (05C38 14H40 14H42)},
  MRNUMBER = {2457739},
       DOI = {10.1090/conm/465/09104},
       URL = {https://doi.org/10.1090/conm/465/09104},
}
@article {arxiv1001.0390,
    AUTHOR = {Miles, Richard and Ward, Thomas},
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   JOURNAL = {Discrete Contin. Dyn. Syst.},
  FJOURNAL = {Discrete and Continuous Dynamical Systems. Series A},
    VOLUME = {30},
      YEAR = {2011},
    NUMBER = {4},
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      ISSN = {1078-0947},
   MRCLASS = {37C40 (37A25 37C35 37C85)},
  MRNUMBER = {2812960 (2012h:37052)},
MRREVIEWER = {Douglas P. Dokken},
       DOI = {10.3934/dcds.2011.30.1181},
       URL = {http://dx.doi.org/10.3934/dcds.2011.30.1181},
}
@book {MR559531,
    AUTHOR = {Milne, James S.},
     TITLE = {\'{E}tale {C}ohomology},
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    VOLUME = {33},
 PUBLISHER = {Princeton University Press},
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     PAGES = {xiii+323},
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   MRCLASS = {14-02 (14F20 18F99)},
  MRNUMBER = {MR559531 (81j:14002)},
MRREVIEWER = {G. Horrocks},
}

@article{milnor:quadraticmaps, 
    AUTHOR = {Milnor, John},
     TITLE = {Geometry and dynamics of quadratic rational maps},
      NOTE = {With an appendix by the author and Lei Tan},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {2},
      YEAR = {1993},
    NUMBER = {1},
     PAGES = {37--83},
      ISSN = {1058-6458},
   MRCLASS = {58F20 (30D05 32S70 58F23)},
  MRNUMBER = {MR1246482 (96b:58094)},
MRREVIEWER = {J. S. Joel},
}

@book {MR2193309,
    AUTHOR = {Milnor, John},
     TITLE = {Dynamics in one complex variable},
    SERIES = {Annals of Mathematics Studies},
    VOLUME = {160},
   EDITION = {Third},
 PUBLISHER = {Princeton University Press, Princeton, NJ},
      YEAR = {2006},
     PAGES = {viii+304},
      ISBN = {978-0-691-12488-9; 0-691-12488-4},
   MRCLASS = {37Fxx (30-01 30D05 37-01)},
  MRNUMBER = {2193309},
}
@book{milnor:dynamicslectures, 
    AUTHOR = {Milnor, John},
     TITLE = {Dynamics in {O}ne {C}omplex {V}ariable},
 PUBLISHER = {Friedr. Vieweg \& Sohn},
   ADDRESS = {Braunschweig},
      YEAR = {1999},
     PAGES = {viii+257},
      ISBN = {3-528-03130-1},
   MRCLASS = {37Fxx (30D05 37-01)},
  MRNUMBER = {MR1721240 (2002i:37057)},
MRREVIEWER = {Dierk Schleicher},
}

@article {MR1806289,
    AUTHOR = {Milnor, John},
     TITLE = {On rational maps with two critical points},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {9},
      YEAR = {2000},
    NUMBER = {4},
     PAGES = {481--522},
      ISSN = {1058-6458},
   MRCLASS = {37F50 (37F20)},
  MRNUMBER = {MR1806289 (2001k:37074)},
MRREVIEWER = {Peter Ha{\"{\i}}ssinsky},
}

@incollection {milnor:lattesmaps,
    AUTHOR = {Milnor, John},
     TITLE = {On {L}att\`es maps},
 BOOKTITLE = {Dynamics on the {R}iemann sphere},
     PAGES = {9--43},
 PUBLISHER = {Eur. Math. Soc., Z\"urich},
      YEAR = {2006},
   MRCLASS = {37F10 (30D05 37-02)},
  MRNUMBER = {MR2348953},
MRREVIEWER = {Feliks Przytycki},
     NOTE = {\url{ArXiv:math.DS/0402147},
             Stony Brook IMS Preprint \#2004/01},
}
@incollection {MR2508263,
    AUTHOR = {Milnor, John},
     TITLE = {Cubic polynomial maps with periodic critical orbit. {I}},
 BOOKTITLE = {Complex dynamics},
     PAGES = {333--411},
 PUBLISHER = {A K Peters},
   ADDRESS = {Wellesley, MA},
      YEAR = {2009},
   MRCLASS = {37Fxx (30D05 32Hxx)},
  MRNUMBER = {2508263},
}

@phdthesis{mimarthesis1997, 
    AUTHOR = {Mimar, A.},
     TITLE = {On the preperiodic points of an endomorphism of $\mathbb{P}^1
          \times\mathbb{P}^1$ which lie on a curve},
   SCHOOL = {Columbia University},
     YEAR = {19997},
}
@comment{UPDATE}
@misc {arxiv2102.07561,
    AUTHOR = {Piotr Miska and Tom Ward},
    TITLE = {Stirling number and periodic points},
     YEAR = {2021},
     NOTE = {\url{arXiv:2102.07561}},
}
@article {MR56619,
    AUTHOR = {Mordell, L. J.},
     TITLE = {On the integer solutions of the equation {$x^2+y^2+z^2+2xyz=n$}},
   JOURNAL = {J. London Math. Soc.},
  FJOURNAL = {The Journal of the London Mathematical Society},
    VOLUME = {28},
      YEAR = {1953},
     PAGES = {500--510},
      ISSN = {0024-6107},
   MRCLASS = {10.0X},
  MRNUMBER = {56619},
MRREVIEWER = {Ivan Niven},
       DOI = {10.1112/jlms/s1-28.4.500},
       URL = {https://doi.org/10.1112/jlms/s1-28.4.500},
}
@article {arxiv1010.0341,
    AUTHOR = {Moret-Bailly, Laurent},
     TITLE = {Un th\'eor\`eme de l'application ouverte sur les corps
              valu\'es alg\'ebriquement clos},
   JOURNAL = {Math. Scand.},
  FJOURNAL = {Mathematica Scandinavica},
    VOLUME = {111},
      YEAR = {2012},
    NUMBER = {2},
     PAGES = {161--168},
      ISSN = {0025-5521},
     CODEN = {MTSCAN},
   MRCLASS = {14Axx},
  MRNUMBER = {3023520},
}
@comment{Open mapping theorem over any valued field}
@article {MR1779799,
    AUTHOR = {Moriwaki, Atsushi},
     TITLE = {Arithmetic height functions over finitely generated fields},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {140},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {101--142},
      ISSN = {0020-9910},
   MRCLASS = {11G50 (11G10 11G35 14G40 14K15)},
  MRNUMBER = {1779799},
MRREVIEWER = {Carlo Gasbarri},
       DOI = {10.1007/s002220050358},
       URL = {https://doi.org/10.1007/s002220050358},
}
@book {MR2158954,
    AUTHOR = {Morris, Dave Witte},
     TITLE = {Ratner's {T}heorems on {U}nipotent {F}lows},
    SERIES = {Chicago Lectures in Mathematics},
 PUBLISHER = {University of Chicago Press},
   ADDRESS = {Chicago, IL},
      YEAR = {2005},
     PAGES = {xii+203},
      ISBN = {0-226-53983-0; 0-226-53984-9},
   MRCLASS = {37A17 (22E40 22F30 37A25 37A30 37A35)},
  MRNUMBER = {MR2158954 (2006h:37006)},
MRREVIEWER = {Bachir Bekka},
}

@article {morton:quadraticmaps,
    AUTHOR = {Morton, Patrick},
     TITLE = {Arithmetic properties of periodic points of quadratic maps},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {62},
      YEAR = {1992},
    NUMBER = {4},
     PAGES = {343--372},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {12E10 (12F10)},
  MRNUMBER = {MR1199627 (93k:12004)},
MRREVIEWER = {R. W. K. Odoni},
}
@article {MR4022234,
    AUTHOR = {Morton, Patrick},
     TITLE = {Periodic points of algebraic functions and {D}euring's class
              number formula},
   JOURNAL = {Ramanujan J.},
  FJOURNAL = {Ramanujan Journal. An International Journal Devoted to the
              Areas of Mathematics Influenced by Ramanujan},
    VOLUME = {50},
      YEAR = {2019},
    NUMBER = {2},
     PAGES = {323--354},
      ISSN = {1382-4090},
   MRCLASS = {11G15 (11D41 11G07 37P05)},
  MRNUMBER = {4022234},
       DOI = {10.1007/s11139-018-0120-x},
       URL = {https://doi.org/10.1007/s11139-018-0120-x},
}
@article {morton:quadraticmaps2,
    AUTHOR = {Morton, Patrick},
     TITLE = {Arithmetic properties of periodic points of quadratic maps.
              {II}},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {87},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {89--102},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11G30 (11F03 14G05)},
  MRNUMBER = {MR1665198 (2000c:11103)},
MRREVIEWER = {Nobuhiko Ishida},
}

@article {morton:galoisperiodicpoints,
    AUTHOR = {Morton, Patrick},
     TITLE = {Galois groups of periodic points},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {201},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {401--428},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {12F10},
  MRNUMBER = {MR1612390 (99a:12005)},
MRREVIEWER = {Tara L. Smith},
}

@article {morton:finitefielddynamics,
    AUTHOR = {Morton, Patrick},
     TITLE = {Periods of maps on irreducible polynomials over finite fields},
   JOURNAL = {Finite Fields Appl.},
  FJOURNAL = {Finite Fields and their Applications},
    VOLUME = {3},
      YEAR = {1997},
    NUMBER = {1},
     PAGES = {11--24},
      ISSN = {1071-5797},
   MRCLASS = {11G99 (11R58)},
  MRNUMBER = {MR1429040 (98d:11075)},
MRREVIEWER = {Joseph H. Silverman},
}

@article {morton:dynamicalmoduli,
    AUTHOR = {Morton, Patrick},
     TITLE = {On certain algebraic curves related to polynomial maps},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {103},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {319--350},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {14H10 (11G99 11R32 58F03)},
  MRNUMBER = {MR1414593 (97m:14030)},
MRREVIEWER = {Joseph H. Silverman},
}
@article {MR2771135,
    AUTHOR = {Morton, Patrick},
     TITLE = {Corrigendum: `{{O}n certain algebraic curves related to
              polynomial maps}, {C}ompositio {M}ath. 103 (1996), 319--350'},
   JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {147},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {332--334},
      ISSN = {0010-437X},
   MRCLASS = {14H10 (11G99 11R32 37Pxx)},
  MRNUMBER = {2771135},
       DOI = {10.1112/S0010437X1000480X},
       URL = {http://dx.doi.org/10.1112/S0010437X1000480X},
}

@article {morton:cubicextensions,
    AUTHOR = {Morton, Patrick},
     TITLE = {Characterizing cyclic cubic extensions by automorphism
              polynomials},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {49},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {183--208},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {12F10 (11R16)},
  MRNUMBER = {MR1305089 (95j:12006)},
MRREVIEWER = {Joseph H. Silverman},
}
@comment{UPDATE}
@misc {arxiv1410.4618,
    AUTHOR = {Morton, Patrick},
    TITLE = {Solutions of diophantine equations as periodic points of
                  $p$-adic algebraic functions, {I}},
     YEAR = {2014},
     NOTE = {\url{arXiv:1410.4618}},
}
@comment{UPDATE}
@misc {arxivarXiv:1806.11079,
    AUTHOR = {Morton, Patrick},
    TITLE = {Solutions of diophantine equations as periodic points of
                  $p$-adic algebraic functions, {II}},
     YEAR = {2018},
     NOTE = {\url{arXiv:arXiv:1806.11079}},
}
@comment{UPDATE}
@misc {arxiv1410.6798,
    AUTHOR = {Morton, Patrick},
    TITLE = {Solutions of the cubic Fermat equation in ring class
                  fields of imaginary quadratic fields (as periodic
                  points of a 3-adic algebraic function)},
     YEAR = {2014},
     NOTE = {\url{arXiv:1410.6798}},
}
@comment{UPDATE}
@misc {arxiv2105.07435,
    AUTHOR = {Morton, Patrick},
    TITLE = {An elementary property of the quadratic map over ${\mathbb{Q}}$},
     YEAR = {2021},
     NOTE = {\url{arXiv:2105.07435}},
}
@article {mortonpatel:galoisperiodicpoints,
    AUTHOR = {Morton, Patrick and Patel, Pratiksha},
     TITLE = {The {G}alois theory of periodic points of polynomial maps},
   JOURNAL = {Proc. London Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {68},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {225--263},
      ISSN = {0024-6115},
     CODEN = {PLMTAL},
   MRCLASS = {11R32 (39B12)},
  MRNUMBER = {MR1253503 (94i:11090)},
MRREVIEWER = {Joseph H. Silverman},
}

@article {mortonsilverman:rationalperiodicpoints,
    AUTHOR = {Morton, Patrick and Silverman, Joseph H.},
     TITLE = {Rational periodic points of rational functions},
   JOURNAL = {Internat. Math. Res. Notices},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {97--110},
      ISSN = {1073-7928},
   MRCLASS = {11G99 (14E05)},
  MRNUMBER = {MR1264933 (95b:11066)},
MRREVIEWER = {Jeffrey Lin Thunder},
}


@article {mortonsilverman:dynamicalunits,
    AUTHOR = {Morton, Patrick and Silverman, Joseph H.},
     TITLE = {Periodic points, multiplicities, and dynamical units},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {461},
      YEAR = {1995},
     PAGES = {81--122},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11G99},
  MRNUMBER = {MR1324210 (96b:11090)},
MRREVIEWER = {Jeffrey Lin Thunder},
}


@article {mortonvivaldi:bifurcations,
    AUTHOR = {Morton, Patrick and Vivaldi, Franco},
     TITLE = {Bifurcations and discriminants for polynomial maps},
   JOURNAL = {Nonlinearity},
  FJOURNAL = {Nonlinearity},
    VOLUME = {8},
      YEAR = {1995},
    NUMBER = {4},
     PAGES = {571--584},
      ISSN = {0951-7715},
     CODEN = {NONLE5},
   MRCLASS = {11C08 (11R21 30D05 58F14 58F23)},
  MRNUMBER = {MR1342504 (96k:11028)},
MRREVIEWER = {Takehiko Morita},
}
@article {MR2249990,
    AUTHOR = {Mosteig, Edward},
     TITLE = {Fixed points of maps on the space of rational functions},
   JOURNAL = {Online J. Anal. Comb.},
  FJOURNAL = {Online Journal of Analytic Combinatorics},
    NUMBER = {1},
      YEAR = {2006},
     PAGES = {Art. 2, 9 pp. (electronic)},
      ISSN = {1931-3365},
   MRCLASS = {26C15 (11R18 37C25)},
  MRNUMBER = {2249990 (2007j:26012)},
MRREVIEWER = {Wadim Zudilin},
}
@article {moussa:integersinjuliasets, 
    AUTHOR = {Moussa, Pierre and Geronimo, Jeffrey S. and Bessis, Daniel},
     TITLE = {Ensembles de {J}ulia et propri\'et\'es de localisation des
              familles it\'er\'ees d'entiers alg\'ebriques},
   JOURNAL = {C.~R.~Acad. Sci. Paris S\'er. I Math.},
  FJOURNAL = {Comptes Rendus des S\'eances de l'Acad\'emie des Sciences.
              S\'erie I. Math\'ematique},
    VOLUME = {299},
      YEAR = {1984},
    NUMBER = {8},
     PAGES = {281--284},
      ISSN = {0249-6291},
     CODEN = {CASMEI},
   MRCLASS = {58F22 (11R06)},
  MRNUMBER = {MR761246 (86f:58133)},
MRREVIEWER = {M. Rees},
}
@comment{ The authors prove that algebraic integers in the filled
Julia set are preperiodic. They formulate a Lehmer-type conjecture for
Green's functions associated to polynomials.  }

@incollection {MR848378,
    AUTHOR = {Moussa, Pierre},
     TITLE = {Ensembles de {J}ulia et propri\'et\'es de localisation des
              entiers alg\'ebriques},
 BOOKTITLE = {Seminar on {N}umber {T}heory, 1984--1985 (Talence, 1984/1985)},
     PAGES = {Exp.\ No.\ 21, 10},
 PUBLISHER = {Univ. Bordeaux I},
   ADDRESS = {Talence},
      YEAR = {1985},
   MRCLASS = {11R04 (11J68 30D05 58F08)},
  MRNUMBER = {MR848378 (87i:11141)},
MRREVIEWER = {I. N. Baker},
}


@incollection {moussa:juliasets, 
    AUTHOR = {Moussa, Pierre},
     TITLE = {Diophantine properties of {J}ulia sets},
 BOOKTITLE = {Chaotic {D}ynamics and {F}ractals (Atlanta, Ga., 1985)},
    SERIES = {Notes Rep. Math. Sci. Engrg.},
    VOLUME = {2},
     PAGES = {215--227},
 PUBLISHER = {Academic Press},
   ADDRESS = {Orlando, FL},
      YEAR = {1986},
   MRCLASS = {58F11 (30D05)},
  MRNUMBER = {MR858017},
}
@comment{UPDATE}
@misc {arxiv1701.00127,
    AUTHOR = {Mukhamedov, Farrukh and Khakimov, Otabek},
    TITLE = {Chaotic behavior of the $P$-adic {P}otts--{B}ethe mapping},
     YEAR = {2017},
     NOTE = {\url{arXiv:1701.00127}},
}
@article {MR2067949,
    AUTHOR = {Mukhamedov, Farruh and Rozikov, Utkir},
     TITLE = {On rational {$p$}-adic dynamical systems},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {10},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {21--31},
      ISSN = {1029-3531},
   MRCLASS = {37F10 (11S85 30D05 30G06 54H20)},
  MRNUMBER = {MR2067949 (2005b:37091)},
}
@comment{Detailed analysis of dynamics of (x+a)/(bx+c)}

@article {MR2423943,
    AUTHOR = {Mukhamedov, F.},
     TITLE = {On the chaotic behavior of a cubic {$p$}-adic dynamical
              system},
   JOURNAL = {Mat. Zametki},
  FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Matematicheskie Zametki},
    VOLUME = {83},
      YEAR = {2008},
    NUMBER = {3},
     PAGES = {468--471},
      ISSN = {0025-567X},
   MRCLASS = {37E99 (11S80 11S85 37B25 37F10)},
  MRNUMBER = {MR2423943 (2009c:37038)},
MRREVIEWER = {Anatoly N. Kochubei},
}
@comment{p-adic dynamics of x^3+ax^3}

@comment{UPDATE}
@misc {arxiv:0712.4049,
    AUTHOR = {Mukhamedov, Farrukh and Rozikov, Utkir},
    TITLE = {On one polynomial $p$-adic dynamical system},
     YEAR = {2007},
 LANGUAGE = {Russian},
     NOTE = {\url{ arXiv:0712.4049}},
}

@incollection {arxiv0608573,
    AUTHOR = {Mukhamedov, Farrukh and Mendes, Jos{\'e} F. F.},
     TITLE = {On chaos of a cubic {$p$}-adic dynamical system},
 BOOKTITLE = {Differential equations, chaos and variational problems},
    SERIES = {Progr. Nonlinear Differential Equations Appl.},
    VOLUME = {75},
     PAGES = {305--315},
 PUBLISHER = {Birkh\"auser},
   ADDRESS = {Basel},
      YEAR = {2008},
   MRCLASS = {37Bxx (12Jxx 37Exx 54H20)},
  MRNUMBER = {MR2409113},
}

@article {arxiv0702697,
    AUTHOR = {Mukhamedov, Farrukh and Mendes, Jos{\'e} F. F.},
     TITLE = {On the chaotic behavior of a generalized logistic {$p$}-adic
              dynamical system},
   JOURNAL = {J. Differential Equations},
  FJOURNAL = {Journal of Differential Equations},
    VOLUME = {243},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {125--145},
      ISSN = {0022-0396},
     CODEN = {JDEQAK},
   MRCLASS = {37B25 (12J12 37D45 54H20)},
  MRNUMBER = {MR2371782 (2009a:37025)},
MRREVIEWER = {Vladimir S. Anashin},
}
@article {MR3582017,
    AUTHOR = {M\"{u}ller, Jan Steffen and Stoll, Michael},
     TITLE = {Canonical heights on genus-2 {J}acobians},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {10},
      YEAR = {2016},
    NUMBER = {10},
     PAGES = {2153--2234},
      ISSN = {1937-0652},
   MRCLASS = {11G50 (11G10 11G30 14G40 14H40 14Q05)},
  MRNUMBER = {3582017},
MRREVIEWER = {Yu Yasufuku},
       DOI = {10.2140/ant.2016.10.2153},
       URL = {https://doi.org/10.2140/ant.2016.10.2153},
}
@article {MR3988813,
    AUTHOR = {M\"{u}ller, J. Steffen and Stumpe, Corinna},
     TITLE = {Archimedean local height differences on elliptic curves},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {190},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {293--303},
      ISSN = {0065-1036},
   MRCLASS = {11G50 (11G05 11G07 14G05)},
  MRNUMBER = {3988813},
MRREVIEWER = {Yu Yasufuku},
       DOI = {10.4064/aa180714-7-12},
       URL = {https://doi.org/10.4064/aa180714-7-12},
}		
@comment{UPDATE}
@misc {arxiv1603.03991,
    AUTHOR = {Mullen, Cara},
    TITLE = {The critical orbit structure of quadratic polynomials in
                  $\mathbb{Z}_p$},
     YEAR = {2016},
     NOTE = {\url{arXiv:1603.03991}},
}
@book {MR0282985,
    AUTHOR = {Mumford, David},
     TITLE = {Abelian {V}arieties},
    SERIES = {Tata Institute of Fundamental Research Studies in Mathematics,
              No. 5 },
 PUBLISHER = {Published for the Tata Institute of Fundamental Research,
              Bombay},
      YEAR = {1970},
     PAGES = {viii+242},
   MRCLASS = {14.51},
  MRNUMBER = {MR0282985 (44 \#219)},
MRREVIEWER = {J. S. Milne},
}



@article {MR0219542,
    AUTHOR = {Mumford, D.},
     TITLE = {On the equations defining abelian varieties. {III}},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {3},
      YEAR = {1967},
     PAGES = {215--244},
      ISSN = {0020-9910},
   MRCLASS = {14.51},
  MRNUMBER = {MR0219542 (36 \#2622)},
MRREVIEWER = {J. W. S. Cassels},
}
@article {MR0219541,
    AUTHOR = {Mumford, D.},
     TITLE = {On the equations defining abelian varieties. {II}},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {3},
      YEAR = {1967},
     PAGES = {75--135},
      ISSN = {0020-9910},
   MRCLASS = {14.51},
  MRNUMBER = {MR0219541 (36 \#2621)},
MRREVIEWER = {J. W. S. Cassels},
}
@article {MR0204427,
    AUTHOR = {Mumford, D.},
     TITLE = {On the equations defining abelian varieties. {I}},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {1},
      YEAR = {1966},
     PAGES = {287--354},
      ISSN = {0020-9910},
   MRCLASS = {14.51},
  MRNUMBER = {MR0204427 (34 \#4269)},
MRREVIEWER = {J. W. S. Cassels},
}

@incollection {MR0437531,
    AUTHOR = {Mumford, David and Suominen, Kalevi},
     TITLE = {Introduction to the theory of moduli},
 BOOKTITLE = {Algebraic {G}eometry, Oslo 1970 (Proc. Fifth Nordic
              Summer-School in Math.)},
     PAGES = {171--222},
 PUBLISHER = {Wolters-Noordhoff},
   ADDRESS = {Groningen},
      YEAR = {1972},
   MRCLASS = {14D20},
  MRNUMBER = {MR0437531 (55 \#10455)},
MRREVIEWER = {H. Popp},
}

@book {mumford:geometricinvarianttheory, 
    AUTHOR = {Mumford, David and Fogarty, John and Kirwan, Frances},
     TITLE = {Geometric {I}nvariant {T}heory},
    SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results
              in Mathematics and Related Areas (2)]},
    VOLUME = {34},
   EDITION = {Third},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1994},
     PAGES = {xiv+292},
      ISBN = {3-540-56963-4},
   MRCLASS = {14D25 (58E05 58F05)},
  MRNUMBER = {MR1304906 (95m:14012)},
MRREVIEWER = {Yi Hu},
}
@book {MR1803093,
    AUTHOR = {Murty, M. Ram},
     TITLE = {Problems in {A}nalytic {N}umber {T}heory},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {206},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {2001},
     PAGES = {xvi+452},
      ISBN = {0-387-95143-1},
   MRCLASS = {11-01 (11M06 11N05)},
  MRNUMBER = {MR1803093 (2001k:11002)},
MRREVIEWER = {D. R. Heath-Brown},
}
@comment{UPDATE}
@misc {arxiv1906.03534,
    AUTHOR = {Murty, M. Ram and Prabhu, Neha},
    TITLE = {The error term in the {S}ato--{T}ate theorem of {B}irch},
     YEAR = {2019},
     NOTE = {\url{arXiv:1906.03534}},
}
@article {MR1395936,
    AUTHOR = {Murty, M. Ram and Rosen, Michael and Silverman, Joseph H.},
     TITLE = {Variations on a theme of {R}omanoff},
   JOURNAL = {Internat. J. Math.},
  FJOURNAL = {International Journal of Mathematics},
    VOLUME = {7},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {373--391},
      ISSN = {0129-167X},
   MRCLASS = {11G05 (11N64 11R47)},
  MRNUMBER = {1395936},
MRREVIEWER = {Henri Darmon},
       DOI = {10.1142/S0129167X96000220},
       URL = {https://doi.org/10.1142/S0129167X96000220},
}
@comment{--NNN-- }
@book {MR2104208,
    AUTHOR = {Nakayama, Noboru},
     TITLE = {Zariski-decomposition and abundance},
    SERIES = {MSJ Memoirs},
    VOLUME = {14},
 PUBLISHER = {Mathematical Society of Japan},
   ADDRESS = {Tokyo},
      YEAR = {2004},
     PAGES = {xiv+277},
      ISBN = {4-931469-31-0},
   MRCLASS = {14C20 (14E15 14E30 14J10)},
  MRNUMBER = {2104208 (2005h:14015)},
MRREVIEWER = {Tommaso De Fernex},
}
@article {narkpreprint03,
    AUTHOR = {Narkiewicz, W. and Marszalek, Roman},
    TITLE = {Finite polynomial orbits in quadratic rings},
   JOURNAL = {J. Ramanujan Math. Soc.},
  FJOURNAL = {Journal of the Ramanujan Mathematical Society},
    VOLUME = {12},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {91--130},
}
@article {MR3447581,
    AUTHOR = {Narkiewicz, W.},
     TITLE = {On a class of monic binomials},
   JOURNAL = {Proc. Steklov Inst. Math.},
  FJOURNAL = {Proceedings of the Steklov Institute of Mathematics},
    VOLUME = {280},
      YEAR = {2013},
    NUMBER = {suppl. 2},
     PAGES = {S65--S70},
      ISSN = {0081-5438},
   MRCLASS = {37P35 (11R09)},
  MRNUMBER = {3447581},
MRREVIEWER = {Lukas Pottmeyer},
       DOI = {10.1134/S0081543813030073},
       URL = {https://doi.org/10.1134/S0081543813030073},
}
@article {narkiewiczcubic,
    AUTHOR = {Narkiewicz, W.},  
     TITLE = {Polynomial cycles in cubic fields of negative discriminant},
   JOURNAL = {Funct. Approx. Comment. Math.},
  FJOURNAL = {Uniwersytet im. Adama Mickiewicza w Poznaniu. Wydzia\l\
              Matematyki i Informatyki. Functiones et Approximatio
              Commentarii Mathematici},
    VOLUME = {35},
      YEAR = {2006},
     PAGES = {261--270},
}
@article {MR2040692,
    AUTHOR = {Narkiewicz, W.},
     TITLE = {Polynomial cycles in certain rings of rationals},
   JOURNAL = {J. Th\'eor. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
    VOLUME = {14},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {529--552},
      ISSN = {1246-7405},
   MRCLASS = {11C08 (11R09 13A99)},
  MRNUMBER = {MR2040692 (2005a:11029)},
MRREVIEWER = {Jean-Luc Chabert},
}
@incollection {MR2001e:11025,
    AUTHOR = {Narkiewicz, W.},
     TITLE = {Finite polynomial orbits. {A} survey},
 BOOKTITLE = {Algebraic {N}umber {T}heory and Diophantine {A}nalysis (Graz, 1998)},
     PAGES = {331--338},
 PUBLISHER = {de Gruyter},
   ADDRESS = {Berlin},
      YEAR = {2000},
   MRCLASS = {11C08 (12F05)},
  MRNUMBER = {2001e:11025},
MRREVIEWER = {Mireille Car},
}

}
@article {narkiewicz:survey,
    AUTHOR = {Narkiewicz, W.},
     TITLE = {Arithmetics of dynamical systems: a survey},
      NOTE = {Number theory (Liptovsk\'y J\'an, 1995)},
   JOURNAL = {Tatra Mt. Math. Publ.},
  FJOURNAL = {Tatra Mountains Mathematical Publications},
    VOLUME = {11},
      YEAR = {1997},
     PAGES = {69--75},
      ISSN = {1210-3195},
   MRCLASS = {11C08 (11R09 11S05)},
  MRNUMBER = {99b:11018},
MRREVIEWER = {Liang-Chung Hsia},
}

@book {MR97e:11037,
    AUTHOR = {Narkiewicz, W.},
     TITLE = {Polynomial {M}appings},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {1600},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1995},
     PAGES = {viii+130},
      ISBN = {3-540-59435-3},
   MRCLASS = {11C08 (12E05 13B25 13F20)},
  MRNUMBER = {MR1367962 (97e:11037)},
MRREVIEWER = {Jean-Luc Chabert},
}

@article {narkiewicz:polynomialcycles,
    AUTHOR = {Narkiewicz, W.},
     TITLE = {Polynomial cycles in algebraic number fields},
   JOURNAL = {Colloq. Math.},
  FJOURNAL = {Colloquium Mathematicum},
    VOLUME = {58},
      YEAR = {1989},
    NUMBER = {1},
     PAGES = {151--155},
      ISSN = {0010-1354},
     CODEN = {CQMAAQ},
   MRCLASS = {11R09 (11C08)},
  MRNUMBER = {90k:11135},
MRREVIEWER = {T. Mets{\"a}nkyl{\"a}},
}

@article {narkiewiczpezda:finiteorbits,
    AUTHOR = {Narkiewicz, W. and Pezda, T.},
     TITLE = {Finite polynomial orbits in finitely generated domains},
   JOURNAL = {Monatsh. Math.},
  FJOURNAL = {Monatshefte f\"ur Mathematik},
    VOLUME = {124},
      YEAR = {1997},
    NUMBER = {4},
     PAGES = {309--316},
      ISSN = {0026-9255},
     CODEN = {MNMTA2},
   MRCLASS = {11R09 (11C08 11S05)},
  MRNUMBER = {99b:11117},
MRREVIEWER = {Liang-Chung Hsia},
}
@comment{UPDATE}
@misc {arxiv1904.12393,
    AUTHOR = {Naskrecki, Bartosz and Streng, Marco},
    TITLE = {Primitive divisors of elliptic divisibility sequences over function fields with constant $j$-invariant},
     YEAR = {2019},
     NOTE = {\url{arXiv:1904.12393}},
}
@comment{UPDATE}
@misc {arxiv2011.08788,
    AUTHOR = {Nasserden, Brett},
    TITLE = {Effective Eigendivisors and the {K}awaguchi--{S}ilverman Conjecture},
     YEAR = {2020},
     NOTE = {\url{arXiv:2011.08788}},
}
@article {MR0179173,
    AUTHOR = {N{\'e}ron, A.},
     TITLE = {Quasi-fonctions et hauteurs sur les vari\'et\'es ab\'eliennes},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {82},
      YEAR = {1965},
     PAGES = {249--331},
      ISSN = {0003-486X},
   MRCLASS = {14.49 (14.51)},
  MRNUMBER = {MR0179173 (31 \#3424)},
MRREVIEWER = {M. Nagata},
}
@book {MR1697859,
    AUTHOR = {Neukirch, J{\"u}rgen<},
     TITLE = {Algebraic number theory},
    SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental
              Principles of Mathematical Sciences]},
    VOLUME = {322},
      NOTE = {Translated from the 1992 German original and with a note by
              Norbert Schappacher,
              With a foreword by G. Harder},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1999},
     PAGES = {xviii+571},
      ISBN = {3-540-65399-6},
   MRCLASS = {11Rxx (11-02 11S15 11S31 14C40)},
  MRNUMBER = {1697859},
MRREVIEWER = {Cornelius Greither},
       DOI = {10.1007/978-3-662-03983-0},
       URL = {http://dx.doi.org/10.1007/978-3-662-03983-0},
}
@unpublished {nevinsrogers:quadmaps,
   AUTHOR = {M. Nevins and T.D. Rogers},
    TITLE = {Quadratic maps as dynamical systems on the $p$-adic numbers},
     YEAR = {March 2000},
     NOTE = {unpublished, \url{www.maths.ex.ac.uk/~mwatkins/zeta/nevins.pdf}},
}
@comment{Nevins indicated that this project was shelved because Nilsson published a paper with more general versions of the main theorems.}

@book {MR546290,
    AUTHOR = {Newstead, P. E.},
     TITLE = {Introduction to {M}oduli {P}roblems and {O}rbit {S}paces},
    SERIES = {Tata Institute of Fundamental Research Lectures on Mathematics
              and Physics},
    VOLUME = {51},
 PUBLISHER = {Tata Institute of Fundamental Research},
   ADDRESS = {Bombay},
      YEAR = {1978},
     PAGES = {vi+183},
      ISBN = {0-387-08851-2},
   MRCLASS = {14-02 (14D20)},
  MRNUMBER = {MR546290 (81k:14002)},
MRREVIEWER = {G. Horrocks},
}
@article {MR3752423,
    AUTHOR = {Nguyen, Khoa D.},
     TITLE = {On certain {D}iophantine equations and the dynamical
              {M}ordell-{L}ang problem},
   JOURNAL = {CMS Notes},
  FJOURNAL = {CMS Notes},
    VOLUME = {50},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {14--15},
      ISSN = {1193-9273},
   MRCLASS = {11D61 (14G05)},
  MRNUMBER = {3752423},
}
@comment{UPDATE}
@misc {arxiv1304.3052,
    AUTHOR = {Nguyen, Khoa},
    TITLE = {Hasse principle and {B}ombieri--{M}asser--{Z}annier height bound
                 for the dynamics of diagonally split polynomial maps},
     YEAR = {2013},
     NOTE = {\url{arXiv:1304.3052}},
}
@comment{UPDATE}
@misc {arxiv2112.14937,
    AUTHOR = {Nguyen, Khoa},
    TITLE = {Transcendence of polynomial canonical heights},
     YEAR = {2022},
     NOTE = {\url{arXiv:2112.14937}},
}
@article {MR3314064,
    AUTHOR = {Nguyen, Khoa D.},
     TITLE = {Algebraic independence of local conjugacies and related
              questions in polynomial dynamics},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {143},
      YEAR = {2015},
    NUMBER = {4},
     PAGES = {1491--1499},
      ISSN = {0002-9939},
   MRCLASS = {11J91 (37F10 37P30)},
  MRNUMBER = {3314064},
       DOI = {10.1090/S0002-9939-2014-12438-5},
       URL = {http://dx.doi.org/10.1090/S0002-9939-2014-12438-5},
}
@article {MR2273670,
    AUTHOR = {Nguyen, Viet-Anh},
     TITLE = {Algebraic degrees for iterates of meromorphic self-maps of
              {${\mathbb P}^k$}},
   JOURNAL = {Publ. Mat.},
  FJOURNAL = {Publicacions Matem\`atiques},
    VOLUME = {50},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {457--473},
      ISSN = {0214-1493},
   MRCLASS = {37F10 (32H50)},
  MRNUMBER = {2273670 (2008h:37050)},
}
@comment{UPDATE}
@misc {arxiv2005.05804,
    AUTHOR = {Nie, Hongming and Okuyama, Y{\^u}suke},
    TITLE = {Crucial curvatures and minimal resultant loci for non-archimedean polynomials},
     YEAR = {2020},
     NOTE = {\url{arXiv:2005.05804}},
}
@article {MR3863055,
    AUTHOR = {Nie, Hongming},
     TITLE = {Rescaling limits in non-{A}rchimedean dynamics},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {185},
      YEAR = {2018},
    NUMBER = {4},
     PAGES = {315--331},
      ISSN = {0065-1036},
   MRCLASS = {37P45 (37P50)},
  MRNUMBER = {3863055},
       DOI = {10.4064/aa170601-22-1},
       URL = {https://doi.org/10.4064/aa170601-22-1},
}
@incollection {MR2042407,
    AUTHOR = {Niederreiter, Harald and Shparlinski, Igor E.},
     TITLE = {Dynamical systems generated by rational functions},
 BOOKTITLE = {Applied Algebra, Algebraic Algorithms and Error-Correcting
              Codes (Toulouse, 2003)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {2643},
     PAGES = {6--17},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2003},
   MRCLASS = {94A45 (11T71 37B10 94-02)},
  MRNUMBER = {MR2042407 (2005a:94047)},
}
@comment{Summary: "We consider dynamical systems generated by
iterations of rational functions over finite fields and residue class
rings. We present a survey of recent developments and outline several
open problems."}

@comment{UPDATE}
@misc {arxiv1304.4491,
    AUTHOR = {Nilsson, Marcus},
    TITLE = {Towards a bifurcation theory for perturbed monomial 
         dynamical systems modulo a prime},
     YEAR = {2013},
     NOTE = {\url{arXiv:1304.4491}},
}

@article {MR2026728,
    AUTHOR = {Nilsson, Marcus},
     TITLE = {Fuzzy cycles of {$p$}-adic monomial dynamical systems},
   JOURNAL = {Far East J. Dyn. Syst.},
  FJOURNAL = {Far East Journal of Dynamical Systems},
    VOLUME = {5},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {149--173},
      ISSN = {0972-1118},
   MRCLASS = {37E99 (12J25 39A11)},
  MRNUMBER = {MR2026728 (2004k:37085)},
MRREVIEWER = {Liang-Chung Hsia},
}

@incollection {MR1838295,
    AUTHOR = {Nilsson, Marcus},
     TITLE = {Distribution of cycles of monomial {$p$}-adic dynamical
              systems},
 BOOKTITLE = {$p$-adic {F}unctional {A}nalysis (Ioannina, 2000)},
    SERIES = {Lecture Notes in Pure and Appl. Math.},
    VOLUME = {222},
     PAGES = {233--242},
 PUBLISHER = {Dekker},
   ADDRESS = {New York},
      YEAR = {2001},
   MRCLASS = {37E99 (11S99 37A45 37A99)},
  MRNUMBER = {MR1838295 (2002d:37065)},
MRREVIEWER = {Anatoly N. Kochubei},
}
@article {MR1769981,
    AUTHOR = {Nilsson, Marcus},
     TITLE = {Cycles of monomial and perturbated monomial {$p$}-adic
              dynamical systems},
   JOURNAL = {Ann. Math. Blaise Pascal},
  FJOURNAL = {Annales Math\'ematiques Blaise Pascal},
    VOLUME = {7},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {37--63},
      ISSN = {1259-1734},
   MRCLASS = {11S80 (37B99 37E99)},
  MRNUMBER = {MR1769981 (2001d:11118)},
MRREVIEWER = {Anatoly N. Kochubei},
}
@article {MR2099883,
    AUTHOR = {Nilsson, Marcus and Nyqvist, Robert},
     TITLE = {The asymptotic number of periodic points of discrete
              {$p$}-adic dynamical systems},
   JOURNAL = {Tr. Mat. Inst. Steklova},
  FJOURNAL = {Trudy Matematicheskogo Instituta Imeni V. A. Steklova.
              Rossi\u\i skaya Akademiya Nauk},
    VOLUME = {245},
      YEAR = {2004},
    NUMBER = {Izbr. Vopr. $p$-adich. Mat. Fiz. i Anal.},
     PAGES = {210--217},
      ISSN = {0371-9685},
   MRCLASS = {37F99 (11S85 37C25)},
  MRNUMBER = {MR2099883 (2005h:37103)},
MRREVIEWER = {Liang-Chung Hsia},
}
@incollection {nishizawa91,
    AUTHOR = {Nishizawa, K. and Sekiguchi, K. and Yoshino, K.},
     TITLE = {Location of algebraic integers and related topics},
 BOOKTITLE = {Dynamical Systems and Related Topics (Nagoya, 1990)},
    SERIES = {Adv. Ser. Dyn. Syst.},
    VOLUME = {9},
     PAGES = {422--450},
 PUBLISHER = {World Sci. Publishing},
      YEAR = {1991},
}
@article {MR0037865,
    AUTHOR = {Niven, Ivan},
     TITLE = {The iteration of certain arithmetic functions},
   JOURNAL = {Canadian J. Math.},
    VOLUME = {2},
      YEAR = {1950},
     PAGES = {406--408},
   MRCLASS = {10.0X},
  MRNUMBER = {MR0037865 (12,318m)},
MRREVIEWER = {H. N. Shapiro},
}
@article{northcott:periodicpoints, 
    AUTHOR = {Northcott, D. G.},
     TITLE = {Periodic points on an algebraic variety},
   JOURNAL = {Ann. of Math. (2)},
    VOLUME = {51},
      YEAR = {1950},
     PAGES = {167--177},
   MRCLASS = {14.0X},
  MRNUMBER = {MR0034607 (11,615c)},
MRREVIEWER = {B. Segre},
}

@incollection {MR1838296,
    AUTHOR = {Nyqvist, Robert},
     TITLE = {Some dynamical systems in finite field extensions of the
              {$p$}-adic numbers},
 BOOKTITLE = {$p$-adic functional analysis (Ioannina, 2000)},
    SERIES = {Lecture Notes in Pure and Appl. Math.},
    VOLUME = {222},
     PAGES = {243--253},
 PUBLISHER = {Dekker},
   ADDRESS = {New York},
      YEAR = {2001},
   MRCLASS = {37E99 (11S85 37B99)},
  MRNUMBER = {MR1838296 (2002d:37066)},
MRREVIEWER = {Anatoly N. Kochubei},
}

@comment{--OOO-- }

@comment{UPDATE}
@misc {arxiv2207.10822,
    AUTHOR = {Oberly, Peter J.},
    TITLE = {An Inner Product on Adelic Measures: With Applications to the {A}rakelov--{Z}hang Pairing},
     YEAR = {2022},
     NOTE = {\url{arXiv:2207.10822}},
}
@article {MR1418355,
    AUTHOR = {Odoni, R. W. K.},
     TITLE = {On the {G}alois groups of iterated generic additive
              polynomials},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
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    VOLUME = {121},
      YEAR = {1997},
    NUMBER = {1},
     PAGES = {1--6},
      ISSN = {0305-0041},
     CODEN = {MPCPCO},
   MRCLASS = {12F10},
  MRNUMBER = {MR1418355 (98g:12004)},
}
@article {MR962740,
    AUTHOR = {Odoni, R. W. K.},
     TITLE = {Realising wreath products of cyclic groups as {G}alois groups},
   JOURNAL = {Mathematika},
  FJOURNAL = {Mathematika. A Journal of Pure and Applied Mathematics},
    VOLUME = {35},
      YEAR = {1988},
    NUMBER = {1},
     PAGES = {101--113},
      ISSN = {0025-5793},
     CODEN = {MTKAAB},
   MRCLASS = {12F10 (20E22)},
  MRNUMBER = {MR962740 (90a:12013)},
MRREVIEWER = {Antonio Jos{\'e} Engler},
}
@article {MR805714,
    AUTHOR = {Odoni, R. W. K.},
     TITLE = {The {G}alois theory of iterates and composites of polynomials},
   JOURNAL = {Proc. London Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {51},
      YEAR = {1985},
    NUMBER = {3},
     PAGES = {385--414},
      ISSN = {0024-6115},
     CODEN = {PLMTAL},
   MRCLASS = {12E10 (11B37 30F10)},
  MRNUMBER = {MR805714 (87c:12005)},
MRREVIEWER = {K. Kiyek},
}
@article {MR813379,
    AUTHOR = {Odoni, R. W. K.},
     TITLE = {On the prime divisors of the sequence {$w\sb {n+1}=1+w\sb
              1\cdots w\sb n$}},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {32},
      YEAR = {1985},
    NUMBER = {1},
     PAGES = {1--11},
      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {11N37 (11B37)},
  MRNUMBER = {MR813379 (87b:11094)},
MRREVIEWER = {W. Narkiewicz},
}
@comment{UPDATE}
@misc {arxiv2209.10436,
    AUTHOR = {O'Dorney, Evan},
    TITLE = {Large orbits on {M}arkoff-type {K3} surfaces over finite fields},
     YEAR = {2022},
     NOTE = {\url{arXiv:2209.10436}},
}
@article {MR992208,
    AUTHOR = {Oesterl{\'e}, Joseph},
     TITLE = {Nouvelles approches du ``th\'eor\`eme'' de {F}ermat},
      NOTE = {S{\'e}minaire Bourbaki, Vol. 1987/88},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {161-162},
      YEAR = {1988},
     PAGES = {Exp.\ No.\ 694, 4, 165--186 (1989)},
      ISSN = {0303-1179},
   MRCLASS = {11D41 (11G05 11N37 14G25)},
  MRNUMBER = {992208 (90g:11038)},
MRREVIEWER = {Toshihiro Hadano},
}
@article {MR2745750,
    AUTHOR = {Okuyama, Y{\^u}suke},
     TITLE = {Nonlinearity of morphisms in non-{A}rchimedean and complex
              dynamics},
   JOURNAL = {Michigan Math. J.},
  FJOURNAL = {Michigan Mathematical Journal},
    VOLUME = {59},
      YEAR = {2010},
    NUMBER = {3},
     PAGES = {505--515},
      ISSN = {0026-2285},
   MRCLASS = {37Pxx (11S80 30D05 30G06 37Fxx)},
  MRNUMBER = {2745750},
       DOI = {10.1307/mmj/1291213954},
       URL = {http://dx.doi.org/10.1307/mmj/1291213954},
}
@article {arxiv1106.3367,
    AUTHOR = {Okuyama, Y{\^u}suke},
     TITLE = {Fekete configuration, quantitative equidistribution and
              wandering critical orbits in non-archimedean dynamics},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {273},
      YEAR = {2013},
    NUMBER = {3-4},
     PAGES = {811--837},
      ISSN = {0025-5874},
     CODEN = {MAZEAX},
   MRCLASS = {11G50 (37F10)},
  MRNUMBER = {3030679},
       DOI = {10.1007/s00209-012-1032-x},
       URL = {http://dx.doi.org/10.1007/s00209-012-1032-x},
}
@article {arxiv1106.3363,
    AUTHOR = {Okuyama, Y{\^u}suke},
    TITLE = {Repelling periodic points and logarithmic 
             equidistribution in non-archimedean dynamics},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {152},
      YEAR = {2012},
    NUMBER = {3},
     PAGES = {267--277},
}
@comment{UPDATE}
@misc {arxiv1302.4303,
    AUTHOR = {Okuyama, Y{\^u}suke},
    TITLE = {Adelic equidistribution, characterization of
                  equidistribution, and a general equidistribution
                  theorem in non-archimedean dynamics},
     YEAR = {2013},
     NOTE = {\url{arXiv:1302.4303}},
}

@comment{arxiv1210.7060}
@incollection {MR3074753,
    AUTHOR = {Okuyama, Y{\^u}suke},
     TITLE = {Approximation of {L}yapunov exponents in non-{A}rchimedean and
              complex dynamics},
 BOOKTITLE = {Topics in finite or infinite dimensional complex analysis},
     PAGES = {217--222},
 PUBLISHER = {Tohoku University Press, Sendai},
      YEAR = {2013},
   MRCLASS = {37Pxx (11S82)},
  MRNUMBER = {3074753},
}
@comment{UPDATE}
@misc {arxiv1307.0887,
    AUTHOR = {Okuyama, Y{\^u}suke},
    TITLE = {Algebraic divisors on the projective line having small 
            diagonals and small heights},
     YEAR = {2013},
     NOTE = {\url{arXiv:1307.0887}},
}
@comment{UPDATE}
@misc {arxiv1309.2479,
    AUTHOR = {Okuyama, Y{\^u}suke},
    TITLE = {Quantitative approximations of the {L}yapunov exponent of a
                  rational function over valued fields},
     YEAR = {2013},
     NOTE = {\url{arXiv:1309.2479}},
}
@comment{arxiv1602.02984}
@article {MR3640601,
    AUTHOR = {Okuyama, Y\^usuke},
     TITLE = {A {M}ahler-type estimate of weighted {F}ekete sums on the
              {B}erkovich projective line},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {178},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {257--272},
      ISSN = {0065-1036},
   MRCLASS = {37P30 (37P50)},
  MRNUMBER = {3640601},
       DOI = {10.4064/aa8437-9-2016},
       URL = {http://dx.doi.org/10.4064/aa8437-9-2016},
}
@article {MR4081106,
    AUTHOR = {Okuyama, Y\^{u}suke},
     TITLE = {Geometric formulas on {R}umely's weight function and crucial
              measure in non-archimedean dynamics},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {376},
      YEAR = {2020},
    NUMBER = {3-4},
     PAGES = {913--956},
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  MRNUMBER = {4081106},
       DOI = {10.1007/s00208-019-01884-7},
       URL = {https://doi.org/10.1007/s00208-019-01884-7},
}
@comment{UPDATE}
@misc {arxiv1805.07668,
    AUTHOR = {Okuyama, Y{\^u}suke},
    TITLE = {An a priori bound of rational functions on the
                  {B}erkovich projective line and its complex
                  counterpart on {$\mathbb{CP}^k$}},
     YEAR = {2018},
     NOTE = {\url{arXiv:1805.07668}},
}
@comment{UPDATE}
@misc {arxiv1508.01589,
    AUTHOR = {Okuyama, Y{\^u}suke and Stawiska, Ma{\l{}}gorzata},
    TITLE = {A characterization of polynomials among rational
                  functions in non-archimedean and complex dynamics},
     YEAR = {2015},
     NOTE = {\url{arXiv:1508.01589}},
}
@comment{UPDATE}
@misc {arxiv2008.02619,
    AUTHOR = {Oliveira, Jos{\'e} Alves and Oliveira, Daniela and Reis, Lucas},
    TITLE = {On iterations of rational functions over perfect fields},
     YEAR = {2020},
     NOTE = {\url{arXiv:2008.02619}},
}
@comment{UPDATE}
@misc {arxiv2206.10679,
    AUTHOR = {Olechnowicz, Matt},
    TITLE = {Dynamically improper hypersurfaces for endomorphisms of projective space},
     YEAR = {2022},
     NOTE = {\url{arXiv:2206.10679}},
}
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@article {arxiv0906.3854,
    AUTHOR = {Ostafe, Alina},
     TITLE = {Multivariate permutation polynomial systems and nonlinear
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}
@article {MR3360335,
    AUTHOR = {Ostafe, Alina and Sha, Min},
     TITLE = {On the quantitative dynamical {M}ordell--{L}ang conjecture},
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       DOI = {10.1016/j.jnt.2015.04.011},
       URL = {http://dx.doi.org/10.1016/j.jnt.2015.04.011},
}
@comment{UPDATE}
@misc {arxiv1505.03957,
    AUTHOR = {Ostafe, Alina},
    TITLE = {On some extensions of the {A}ilon--{R}udnick Theorem},
     YEAR = {2015},
     NOTE = {\url{arXiv:1505.03957}},
}
@comment{arxiv1505.03618}
@incollection {MR3546669,
    AUTHOR = {Ostafe, Alina and Sha, Min},
     TITLE = {Counting dynamical systems over finite fields},
 BOOKTITLE = {Dynamics and numbers},
    SERIES = {Contemp. Math.},
    VOLUME = {669},
     PAGES = {187--203},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2016},
   MRCLASS = {37P05 (05A15 37P25)},
  MRNUMBER = {3546669},
MRREVIEWER = {Marc Munsch},
       URL = {https://doi.org/10.1090/conm/669/13429},
}
@comment{UPDATE}
@misc {arxiv1109.0575,
    AUTHOR = {Ostafe, Alina and Shparlinski, Igor},
    TITLE = {Degree Growth, Linear Independence and Periods of a Class
                  of Rational Dynamical Systems},
     YEAR = {2011},
     NOTE = {\url{arXiv:1109.0575}},
}
@comment{UPDATE}
@misc {arxiv0902.3884,
    AUTHOR = {Ostafe, Alina and Shparlinski, Igor},
    TITLE = {On the degree growth in some polynomial dynamical systems and
          nonlinear pseudorandom number generators},
     YEAR = {2009},
     NOTE = {\url{arXiv:0902.3884}},
}
@comment{arXiv:0909.3972}
@article {MR2644881,
    AUTHOR = {Ostafe, Alina and Shparlinski, Igor E.},
     TITLE = {On the length of critical orbits of stable quadratic
              polynomials},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {138},
      YEAR = {2010},
    NUMBER = {8},
     PAGES = {2653--2656},
      ISSN = {0002-9939},
   MRCLASS = {11L40 (11T06 37P25)},
  MRNUMBER = {2644881},
MRREVIEWER = {Thomas Ward},
       URL = {https://doi.org/10.1090/S0002-9939-10-10404-3},
}
@comment{arxiv1001.1504}
@article {MR2765701,
    AUTHOR = {Ostafe, Alina and Shparlinski, Igor E.},
     TITLE = {Pseudorandomness and dynamics of {F}ermat quotients},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
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    NUMBER = {1},
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  MRNUMBER = {2765701},
       DOI = {10.1137/100798466},
       URL = {http://dx.doi.org/10.1137/100798466},
}
@comment{UPDATE}
@misc {arxiv1706.05874,
    AUTHOR = {Ostafe, Alina and Sha, Min and Shparlinski, Igor and Zannier, Umberto},
    TITLE = {On multiplicative dependence of values of rational functions},
     YEAR = {2017},
     NOTE = {\url{arXiv:1706.05874}},
}
@incollection {MR3676410,
    AUTHOR = {Ostafe, Alina and Shparlinski, Igor E.},
     TITLE = {Orbits of algebraic dynamical systems in subgroups and
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     PAGES = {347--368},
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      YEAR = {2017},
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  MRNUMBER = {3676410},
MRREVIEWER = {Joseph H. Silverman},
}
@comment{arxiv1807.11645}
@article {MR4068295,
    AUTHOR = {Ostafe, Alina and Young, Marley},
     TITLE = {On algebraic integers of bounded house and preperiodicity in
              polynomial semigroup dynamics},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {373},
      YEAR = {2020},
    NUMBER = {3},
     PAGES = {2191--2206},
      ISSN = {0002-9947},
   MRCLASS = {11R18 (37F44 37P05)},
  MRNUMBER = {4068295},
       DOI = {10.1090/tran/7974},
       URL = {https://doi.org/10.1090/tran/7974},
}

@comment{--PPP-- }

@comment{UPDATE}
@misc {arxiv2104.11175,
    AUTHOR = {Pagano, Carlo},
    TITLE = {The size of arboreal images, {I}: exponential lower bounds for {PCF} and unicritical polynomials},
     YEAR = {2021},
     NOTE = {\url{arXiv:2104.11175}},
}
@comment{UPDATE}
@misc {arxiv2111.12930,
    AUTHOR = {Palimar, Sushma},
    TITLE = {Prime specialization and iterates of composition of Polynomials},
     YEAR = {2021},
     NOTE = {\url{arXiv:2111.12930}},
}
@article {MR2883082,
    AUTHOR = {Pakapongpun, Apisit},
     TITLE = {Orbit {D}irichlet series for power of maps},
   JOURNAL = {Int. J. Pure Appl. Math.},
  FJOURNAL = {International Journal of Pure and Applied Mathematics},
    VOLUME = {71},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {99--104},
      ISSN = {1311-8080},
   MRCLASS = {11M41},
  MRNUMBER = {2883082},
}
@article {arxiv0901.2646,
    AUTHOR = {Pakapongpun, Apisit and Ward, Thomas},
     TITLE = {Functorial orbit counting},
   JOURNAL = {J. Integer Seq.},
  FJOURNAL = {Journal of Integer Sequences},
    VOLUME = {12},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {Article 09.2.4, 20},
      ISSN = {1530-7638},
   MRCLASS = {11B83},
  MRNUMBER = {MR2486259},
}
@comment{UPDATE}
@misc {arxiv1001.0314,
    AUTHOR = {Pakapongpun, Apisit and Ward, Thomas},
    TITLE = {Orbits for products of maps},
     YEAR = {2010},
     NOTE = {\url{arXiv:1001.0314}},
}

@comment{UPDATE}
@misc {arxiv1108.1900,
    AUTHOR = {Pakovich, Fedor},
    TITLE = {On semiconjugate rational functions },
     YEAR = {2011},
     NOTE = {\url{arXiv:1108.1900}},
}
@comment{UPDATE}
@misc {arxiv1505.06351,
    AUTHOR = {Pakovich, Fedor},
    TITLE = {Polynomial semiconjugacies, decompositions of iterations,
                  and invariant curves},
     YEAR = {2015},
     NOTE = {\url{arXiv:1505.06351}},
}
@comment{UPDATE}
@misc {arxiv1801.01985,
    AUTHOR = {Pakovich, Fedor},
    TITLE = {Algebraic curves $A\circ l(x)-U(y)=0$ and arithmetic of orbits of rational functions},
     YEAR = {2017},
     NOTE = {\url{arXiv:1801.01985}},
}
@article {MR2434164,
    AUTHOR = {Pakovich, Fedor},
     TITLE = {Conservative polynomials and yet another action of
                  {$\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$}
                  on plane trees},
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  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
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      YEAR = {2008},
    NUMBER = {1},
     PAGES = {205--218},
      ISSN = {1246-7405},
   MRCLASS = {11C08 (11R32 20E08)},
  MRNUMBER = {2434164 (2009e:11048)},
MRREVIEWER = {Michael E. Zieve},
}

@article {pal07,
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  MRNUMBER = {MR2148073 (2006c:11070)},
MRREVIEWER = {Mihran Papikian},
}
@comment{UPDATE}
@misc {arxiv1212.5698,
    AUTHOR = {Pan, Ivan and Rittatore, Alvaro},
    TITLE = {Some remarks about the {Z}ariski topology of the {C}remona group},
     YEAR = {2012},
     NOTE = {\url{arXiv:1212.5698}},
}
@article {MR3086161,
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     TITLE = {Arithmetic dynamics and dynamical units},
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  FJOURNAL = {East-West Journal of Mathematics},
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    NUMBER = {2},
     PAGES = {201--207},
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   MRCLASS = {37C25},
  MRNUMBER = {3086161},
}
@comment{UPDATE}
@misc {arxiv2105.03715,
    AUTHOR = {Panraksa, Chatchawan},
    TITLE = {Rational Periodic Points of {$x^d+c$} and $abc$ Conjecture},
     YEAR = {2021},
     NOTE = {\url{arXiv:2105.03715}},
}
@article {arxiv1103.5473,
    AUTHOR = {Panti, Giovanni},
     TITLE = {Denominator-preserving maps},
   JOURNAL = {Aequationes Math.},
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   MRCLASS = {28D05 (11K06)},
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       DOI = {10.1007/s00010-011-0102-1},
       URL = {http://dx.doi.org/10.1007/s00010-011-0102-1},
}
@comment{UPDATE}
@misc {arXiv:2007.12252,
    AUTHOR = {Pareschi, Giuseppe},
    TITLE = {$n$-torsion points on theta divisors and semihomogeneous vector bundles},
     YEAR = {2020},
     NOTE = {\url{arXiv:2007.12252}},
}
@manual{PARI2,
      organization = "{The PARI~Group}",
      title        = "{PARI/GP version {\tt 2.9.0}}",
      year         = 2016,
      address      = "Univ. Bordeaux",
      note         = "available from \url{http://pari.math.u-bordeaux.fr/}"
    }
@article {MR3081000,
    AUTHOR = {Pazuki, Fabien},
     TITLE = {Minoration de la hauteur de {N}\'{e}ron-{T}ate sur les surfaces
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      YEAR = {2013},
    NUMBER = {1-2},
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  MRNUMBER = {3081000},
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       DOI = {10.1007/s00229-012-0593-7},
       URL = {https://doi.org/10.1007/s00229-012-0593-7},
}
@comment{arxiv0911.1913}
@article {MR2645156,
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     TITLE = {Zhang's conjecture and squares of abelian surfaces},
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      YEAR = {2010},
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     PAGES = {483--486},
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  MRNUMBER = {2645156 (2011f:37163)},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.1016/j.crma.2010.03.014},
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}
@article {arxiv1106.1784,
    AUTHOR = {Pazuki, F.},
     TITLE = {Polarized morphisms between abelian varieties},
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      YEAR = {2013},
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   MRCLASS = {37Pxx (14G40)},
  MRNUMBER = {3005555},
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       URL = {http://dx.doi.org/10.1142/S1793042112501394},
}
@comment{UPDATE}
@misc {arxiv2006.13604,
    AUTHOR = {Pazuki, Fabien and Widmer, Martin},
    TITLE = {Bertini and {N}orthcott},
     YEAR = {2020},
     NOTE = {\url{arXiv:2006.13604}},
}
@incollection {MR1913468,
    AUTHOR = {Peinado, A. and Montoya, F. and Mu{\~n}oz, J. and Yuste, A.
              J.},
     TITLE = {Maximal periods of {$x\sp 2+c$} in {$\mathbb{F}\sb q$}},
 BOOKTITLE = {Applied Algebra, Algebraic Algorithms and Error-Correcting
              Codes (Melbourne, 2001)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {2227},
     PAGES = {219--228},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2001},
   MRCLASS = {94A55 (11T71 94A60)},
  MRNUMBER = {MR1913468 (2003d:94065)},
}
@comment{Summary: "The orbits produced by the iterations of the mapping
$x\mapsto x^2+c$, defined over $\mathbb{F}_q$, are studied. Several upper
bounds for their periods are obtained, depending on the coefficient
$c$ and the number of elements $q$."}

@article {percival:chaoticmotion,
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    NUMBER = {1-3},
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     CODEN = {PDNPDT},
   MRCLASS = {58F13},
  MRNUMBER = {MR887460 (88g:58120)},
MRREVIEWER = {Richard Cushman},
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@article {MR637984,
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      YEAR = {1981},
    NUMBER = {2},
     PAGES = {475--488},
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@article {MR540634,
    AUTHOR = {Peters, Justin},
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  FJOURNAL = {Advances in Mathematics},
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      YEAR = {1979},
    NUMBER = {1},
     PAGES = {1--13},
      ISSN = {0001-8708},
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   MRCLASS = {28D20 (22D40)},
  MRNUMBER = {540634 (80i:28037)},
MRREVIEWER = {Robert J. Zimmer},
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}
@article {MR2779260,
    AUTHOR = {Petersen, Karl and Varchenko, Alexander},
     TITLE = {The {E}uler adic dynamical system and path counts in the
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  MRNUMBER = {2779260},
       DOI = {10.3836/tjm/1296483473},
       URL = {http://dx.doi.org/10.3836/tjm/1296483473},
}
@article {MR3394116,
    AUTHOR = {Petsche, Clayton},
     TITLE = {On the distribution of orbits in affine varieties},
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      YEAR = {2015},
    NUMBER = {7},
     PAGES = {2231--2241},
      ISSN = {0143-3857},
   MRCLASS = {37P35 (37P50 37P55)},
  MRNUMBER = {3394116},
MRREVIEWER = {Adam David Towsley},
       DOI = {10.1017/etds.2014.26},
       URL = {https://doi.org/10.1017/etds.2014.26},
}
@article {MR2439640,
    AUTHOR = {Petsche, Clayton},
     TITLE = {{$S$}-integral preperiodic points by dynamical systems over
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  FJOURNAL = {Bulletin of the London Mathematical Society},
    VOLUME = {40},
      YEAR = {2008},
    NUMBER = {5},
     PAGES = {749--758},
      ISSN = {0024-6093},
   MRCLASS = {11G50 (11R04 37P30 37P40)},
  MRNUMBER = {MR2439640 (2010a:11124)},
MRREVIEWER = {Matthew H. Baker},
       DOI = {10.1112/blms/bdn053},
       URL = {http://dx.doi.org/10.1112/blms/bdn053},
}

@article {MR2672310,
    AUTHOR = {Petsche, Clayton},
     TITLE = {A criterion for weak convergence on {B}erkovich projective
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    VOLUME = {348},
      YEAR = {2010},
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       URL = {http://dx.doi.org/10.1007/s00208-010-0485-7},
}
@comment{UPDATE}
@misc {arxiv1810.06708,
    AUTHOR = {Petsche, Clayton},
    TITLE = {Attractors associated to a family of hyperbolic $p$-adic plane automorphisms},
     YEAR = {2018},
     NOTE = {\url{arXiv:1810.06708}},
}

@article {MR3293730,
    AUTHOR = {Petsche, Clayton and Stout, Brian},
     TITLE = {On quadratic rational maps with prescribed good reduction},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {143},
      YEAR = {2015},
    NUMBER = {3},
     PAGES = {1145--1158},
      ISSN = {0002-9939},
   MRCLASS = {37P15 (14G25 37P05)},
  MRNUMBER = {3293730},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.1090/S0002-9939-2014-12291-X},
       URL = {http://dx.doi.org/10.1090/S0002-9939-2014-12291-X},
}
@comment{UPDATE}
@misc {arxiv1303.5783,
    AUTHOR = {Petsche, Clayton and Stout, Brian},
    TITLE = {Global minimal models for endomorphisms of projective space},
     YEAR = {2013},
     NOTE = {\url{arXiv:1303.5783}},
}

@comment{arxiv0806.1364}
@article {MR2567424,
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@article {arxiv0911.1875,
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@comment{arxiv1901.07661}
@article {MR3958063,
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@article {MR1875166,
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@comment{UPDATE}
@misc {arxiv1806.11437,
    AUTHOR = {Peyre, Emmanuel},
    TITLE = {Beyond heights: slopes and distribution of rational points},
     YEAR = {2018},
     NOTE = {\url{arXiv:1806.11437}},
}

@article {pezda:rationalcycles,
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}
@article {MR1943028,
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@article {MR3645573,
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@article{pila:andreoort11, 
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@comment{UPDATE}
@comment{The main purpose of this work is to prove the Andre-Oort conjecture in full generality}
@misc {arxiv2109.08788,
    AUTHOR = {Jonathan Pila and Ananth Shankar and Jacob Tsimerman and H{\'e}l{\`e}ne Esnault and Michael Groechenig},
    TITLE = {Canonical Heights on {S}himura Varieties and the {A}ndr{\'e}--{O}ort Conjecture},
     YEAR = {2021},
     NOTE = {\url{arXiv:2109.08788}},
}


@comment{UPDATE}
@misc {arxiv0610737,
    AUTHOR = {Pineiro, Jorge},
    TITLE = {Mahler formula on the projective $n$-space},
     YEAR = {2006},
     NOTE = {\url{ArXiv:math.NT/0610737}},
}
@comment{UPDATE}
@misc {arxiv1909.03507,
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    TITLE = {Hyperbolic polarized dynamics, pairs of inverse maps and the {D}irichlet property},
     YEAR = {2019},
     NOTE = {\url{arXiv:1909.03507}},
}
@comment{26 pages}
@book {MR2706852,
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      NOTE = {Thesis (Ph.D.)--City University of New York},
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@article {MR2508937,
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@incollection {szpiro04,
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  MRNUMBER = {MR2166086 (2006f:14026)},
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@comment{UPDATE}
@misc {arxiv1303.4940,
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}
@comment{UPDATE}
@misc {arxiv1303.4938,
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     NOTE = {\url{arXiv:1303.4938}},
}
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}
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@comment{arxiv1703.09292}
@article {MR3777538,
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@COMMENT{MR1617987}
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@incollection {MR2041072,
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@comment{UPDATE}
@misc {arxiv1206.7104,
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     YEAR = {2012},
     NOTE = {\url{arXiv:1206.7104}},
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@comment{arxiv1307.5887}
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}
@article {MR3104552,
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}
@comment{UPDATE}
@misc {arxiv1210.3720,
    AUTHOR = {Poonen, Bjorn and Testa, Damiano and van Luijk, Ronald},
    TITLE = {Computing {N}{\'e}ron--{S}everi groups and cycle class groups},
     YEAR = {2012},
     NOTE = {\url{arXiv:1210.3720}},
}
@comment{UPDATE}
@misc {arxiv2201.08480,
    AUTHOR = {Poineau, J{\'e}r{\^o}me},
    TITLE = {Dynamique analytique sur ${\mathbb{Z}}$. {I}: Mesures d'{\'e}quilibre sur une droite projective relative},
     YEAR = {2022},
     NOTE = {\url{arXiv:2201.08480}},
}
@comment{UPDATE}
@misc {arxiv2207.01574,
    AUTHOR = {Poineau, J{\'e}r{\^o}me},
    TITLE = {Dynamique analytique sur ${\mathbb{Z}}$. {II}: {\'E}cart uniforme entre Latt{\`e}s et conjecture de Bogomolov---Fu--Tschinkel},
     YEAR = {2022},
     NOTE = {\url{arXiv:2207.01574}},
}
@article {MR2496235,
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      ISSN = {0016-2736},
   MRCLASS = {37F10 (37E15)},
  MRNUMBER = {2496235},
MRREVIEWER = {Masayo Fujimura},
       DOI = {10.4064/fm203-2-2},
       URL = {https://doi.org/10.4064/fm203-2-2},
}
@comment{UPDATE}
@misc {arxiv1103.1294,
    AUTHOR = {Pottmeyer, Lukas},
    TITLE = {A Dynamical {B}ogomolov Property},
     YEAR = {2011},
     NOTE = {\url{arXiv:1103.1294}},
}
@comment{UPDATE}
@misc {arxiv1201.3327,
    AUTHOR = {Pottmeyer, Lukas},
    TITLE = {An Effective Dynamical {B}ogomolov Property},
     YEAR = {2011},
     NOTE = {\url{arXiv:1201.3327}},
}
@comment{UPDATE}
@misc {arxiv1206.2456,
    AUTHOR = {Pottmeyer, Lukas},
    TITLE = {Heights and totally real numbers},
     YEAR = {2012},
     NOTE = {\url{arXiv:1206.2456}},
}
@comment{arxiv1504.04985}
@article {MR3416948,
    AUTHOR = {Pottmeyer, Lukas},
     TITLE = {Heights and totally {$p$}-adic numbers},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {171},
      YEAR = {2015},
    NUMBER = {3},
     PAGES = {277--291},
      ISSN = {0065-1036},
   MRCLASS = {37P30 (11R04 11S82)},
  MRNUMBER = {3416948},
MRREVIEWER = {Rafe Jones},
       DOI = {10.4064/aa171-3-5},
       URL = {https://doi.org/10.4064/aa171-3-5},
}
@comment{UPDATE}
@misc {arxiv1208.5850,
    AUTHOR = {Pulita, Andrea and  Poineau, J{\'e}r{\^o}me},
    TITLE = {Finiteness of the convergence {N}ewton polygon of an
                  ultrametric linear differential equation over the
                  {B}erkovich affine line},
     YEAR = {2012},
     NOTE = {\url{arXiv:1208.5850}},
}

@article {MR1873399,
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     PAGES = {Article 01.2.1, 18 pp. (electronic)},
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   MRCLASS = {11B83},
  MRNUMBER = {MR1873399 (2002i:11026)},
MRREVIEWER = {Manfred Einsiedler},
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@article {MR1866354,
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  MRNUMBER = {MR1866354 (2002j:37020)},
MRREVIEWER = {Ali Messaoudi},
}

@comment{--QQQ-- }

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   MRCLASS = {58F07 (82A99)},
  MRNUMBER = {MR924318 (88m:58084)},
MRREVIEWER = {Peter L. Christiansen},
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     TITLE = {Integrable mappings and soliton equations. {II}},
   JOURNAL = {Phys. D},
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    VOLUME = {34},
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@comment{The first integrable map of the plane was introduced by
E. M. McMillan \ref[in Topics in modern physics: a tribute to
E. U. Condon, 219--244, Colorado Assoc. Univ. Press, Boulder, CO,
1971], and contained 6 arbitrary parameters. This map was generalized
to an 18-parameter map, that is now commonly called the QRT map.}

@comment{arxiv1901.01088}
@article {MR3991416,
    AUTHOR = {Qureshi, Claudio and Reis, Lucas},
     TITLE = {Dynamics of the {$a$}-map over residually finite {D}edekind
              domains and applications},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {204},
      YEAR = {2019},
     PAGES = {134--154},
      ISSN = {0022-314X},
   MRCLASS = {37P25 (13F05)},
  MRNUMBER = {3991416},
MRREVIEWER = {John R. Doyle},
       DOI = {10.1016/j.jnt.2019.03.018},
       URL = {https://doi.org/10.1016/j.jnt.2019.03.018},
}
@comment{--RRR-- }

@comment{UPDATE}
@misc {arxiv2008.10095,
    AUTHOR = {Ramadas, Rohini and Silversmith, Rob},
    TITLE = {Quadratic rational maps with a five-periodic critical point},
     YEAR = {2020},
     NOTE = {\url{arXiv:2008.10095}},
}
@comment{UPDATE}
@misc {arxiv2205.07349,
    AUTHOR = {Ramadas, Rohini},
    TITLE = {Moduli spaces of quadratic maps: arithmetic and geometry},
     YEAR = {2022},
     NOTE = {\url{arXiv:2205.07349}},
}
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MRREVIEWER = {Matthew H. Baker},
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@comment{rees:deg2moduli}
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@comment{rees:deg2moduli2}
@article{MR1317518,
    AUTHOR = {Rees, Mary},
     TITLE = {A partial description of the parameter space of rational maps
              of degree two. {II}},
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@article {MR3276366,
    AUTHOR = {Reeve-Black, Heather and Vivaldi, Franco},
     TITLE = {Asymptotics in a family of linked strip maps},
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  FJOURNAL = {Physica D. Nonlinear Phenomena},
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@comment{UPDATE}
@misc {arxiv2105.09814,
    AUTHOR = {Reis, Lucas},
    TITLE = {Counting distinct functional graphs from linear finite dynamical systems},
     YEAR = {2021},
     NOTE = {\url{arXiv:2105.09814}},
}
@comment{UPDATE}
@misc {arxiv1609.09379,
    AUTHOR = {Reis, Lucas},
    TITLE = {Nilpotent linearized polynomials over finite fields and applications},
     YEAR = {2016},
     NOTE = {\url{arXiv:1609.09379}},
}
@comment{UPDATE}
@misc {arxiv1810.07715,
    AUTHOR = {Reis, Lucas},
    TITLE = {On the factorization of iterated polynomials},
     YEAR = {2018},
     NOTE = {\url{arXiv:1810.07715}},
}
@article {MR4076922,
    AUTHOR = {Reis, Lucas and Wang, Qiang},
     TITLE = {The dynamics of permutations on irreducible polynomials},
   JOURNAL = {Finite Fields Appl.},
  FJOURNAL = {Finite Fields and their Applications},
    VOLUME = {64},
      YEAR = {2020},
     PAGES = {101664},
      ISSN = {1071-5797},
   MRCLASS = {12E20 (11T06 11T55 37P05)},
  MRNUMBER = {4076922},
       DOI = {10.1016/j.ffa.2020.101664},
       URL = {https://doi.org/10.1016/j.ffa.2020.101664},
}
@comment{UPDATE}
@misc {arxiv1807.05495,
    AUTHOR = {Ren, Rufei},
    TITLE = {Iteration of Polynomials {$AX^d+C$} Over Finite Fields},
     YEAR = {2018},
     NOTE = {\url{arXiv:1807.05495}},
}
@article {MR3418206,
    AUTHOR = {Ren, Qingchun and Richter-Gebert, J\"{u}rgen and Sturmfels, Bernd},
     TITLE = {Cayley-{B}acharach formulas},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {American Mathematical Monthly},
    VOLUME = {122},
      YEAR = {2015},
    NUMBER = {9},
     PAGES = {845--854},
      ISSN = {0002-9890},
   MRCLASS = {14H50 (51N35 68U05 68W30)},
  MRNUMBER = {3418206},
MRREVIEWER = {Ragni Piene},
       DOI = {10.4169/amer.math.monthly.122.9.845},
       URL = {https://doi.org/10.4169/amer.math.monthly.122.9.845},
}
@misc {ressayre08,
    AUTHOR = {Ressayre, Nicolas},
    TITLE = {Reading ``The space of Rational maps on $\mathbb{P}^1$'' 
      by J.H. Silverman, An Introduction to Geometric Invariant Theory},
     YEAR = {2008},
     NOTE = {Cours de 9h donn\'e aux Ultrametric Dynamical Days
       du 14 janvier au 1 F\'evrier 2008 a Santiago du Chili,
       \url{http://www.math.univ-montp2.fr/~ressayre/chili.pdf}},
}
@article {MR2312276,
    AUTHOR = {Rice, Brian},
     TITLE = {Primitive prime divisors in polynomial arithmetic dynamics},
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   MRCLASS = {11B83 (11A41)},
  MRNUMBER = {MR2312276 (2008e:11030)},
MRREVIEWER = {Thomas Ward},
}

@article {MR1501186,
    AUTHOR = {Ritt, J. F.},
     TITLE = {Periodic functions with a multiplication theorem},
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  MRNUMBER = {MR1501186},
}
@article {MR1501252,
    AUTHOR = {Ritt, J. F.},
     TITLE = {Permutable rational functions},
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}

@article {MR2018827,
    AUTHOR = {Rivera-Letelier, Juan},
     TITLE = {Espace hyperbolique {$p$}-adique et dynamique des fonctions
              rationnelles},
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@article {MR1937110,
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@comment{UPDATE} 
@misc {arxiv0412180,
    AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Sur la structure des ensembles de {F}atou $p$-adiques},
     YEAR = {2002},
     NOTE = {\url{ArXiv:math.DS/0412180}},
}
@comment{35 pages  Should this be changed to unpublished?}

@article {arxiv0406417,
   AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Wild recurrent critical points},
  JOURNAL = {J. London Math. Soc. (2)},
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   VOLUME = {72},
     YEAR = {2005},
   NUMBER = {2},
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     ISSN = {0024-6107},
    CODEN = {JLMSAK},
  MRCLASS = {37F50 (11S85 37F10)},
 MRNUMBER = {MR2156656 (2006f:37066)},
MRREVIEWER = {Serge Cantat},
}
@comment{\url{ArXiv:math.DS/0406417}}

@comment{UPDATE}
@misc {arxiv0605676,
    AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Notes sur la droite projective de {B}erkovich},
     YEAR = {2006},
     NOTE = {\url{ArXiv:math.MG/0605676}},
}
@comment{47 pages? Should this be changed to unpublished?}

@article {riverappt1,
   AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Points p\'eriodiques des fonctions rationnelles dans l'espace
             hyperbolique {$p$}-adique},
  JOURNAL = {Comment. Math. Helv.},
 FJOURNAL = {Commentarii Mathematici Helvetici. A Journal of the Swiss
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   VOLUME = {80},
     YEAR = {2005},
   NUMBER = {3},
    PAGES = {593--629},
     ISSN = {0010-2571},
  MRCLASS = {37F10 (11S85 37C25 37E99)},
 MRNUMBER = {MR2165204 (2006d:37081)},
MRREVIEWER = {Serge Cantat},
}


@comment{UPDATE}
@misc {riverappt2,
    AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Polynomials over {$\mathbb{C}_p$} with wandering domains, 
        after {R}. {B}enedetto},
     YEAR = {2006},
     NOTE = {Preprint, \url{www.math.sunysb.edu/~rivera/mypapers/wand.ps}},
}

@comment{UPDATE}
@misc {riverappt3,
    AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Th\'eorie de {F}atou et {J}ulia dans la droite projective de
            {B}erkovich},
     YEAR = {2007},
     NOTE = {In preparation},
}

@phdthesis{riverathesis, 
    AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Dynamique des fonctions rationnelles sur des corps locaux},
   SCHOOL = {Universite de {Paris} {X}{I}},
     YEAR = {2000}
}

@article {MR2040006,
    AUTHOR = {Rivera-Letelier, Juan},
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MRREVIEWER = {Serge Cantat},
}
@comment{This is essentially the author's thesis}

@article {MR69328,
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@comment{UPDATE}
@misc {arxiv2104.06407,
    AUTHOR = {Robins, Sinai},
    TITLE = {A friendly invitation to {F}ourier analysis on polytopes},
     YEAR = {2021},
     NOTE = {\url{arXiv:2104.06407}},
}
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@article {MR2415046,
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@article {MR2892428,
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   JOURNAL = {Amer. Math. Monthly},
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}
@article {MR4017941,
    AUTHOR = {Rout, Sudhansu Sekhar},
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   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {207},
      YEAR = {2020},
     PAGES = {122--137},
      ISSN = {0022-314X},
   MRCLASS = {37P55 (11B37 11D61)},
  MRNUMBER = {4017941},
       DOI = {10.1016/j.jnt.2019.07.003},
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}
@comment{UPDATE}
@misc {arxiv2102.04077,
    AUTHOR = {Rout, Sudhansu Sekhar},
    TITLE = {Reduction of polynomial dynamical systems modulo primes},
     YEAR = {2021},
     NOTE = {\url{arXiv:2102.04077}},
}
@comment{UPDATE}
@misc {arxiv2102.04073,
    AUTHOR = {Rout, Sudhansu Sekhar},
    TITLE = {The orbit intersection problem in positive characteristic},
     YEAR = {2021},
     NOTE = {\url{arXiv:2102.04073}},
}


@article {MR3908961,
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     TITLE = {{$p$}-adic dynamical systems of the function {$\frac{ax}{x^2+
              a}^*$}},
   JOURNAL = {p-Adic Numbers Ultrametric Anal. Appl.},
  FJOURNAL = {p-Adic Numbers, Ultrametric Analysis, and Applications},
    VOLUME = {11},
      YEAR = {2019},
    NUMBER = {1},
     PAGES = {77--87},
      ISSN = {2070-0466},
   MRCLASS = {37P05},
  MRNUMBER = {3908961},
       DOI = {10.1134/S2070046619010059},
       URL = {https://doi.org/10.1134/S2070046619010059},
}
@article {MR2106974,
    AUTHOR = {Ru, Min and Yi, Eunjeong},
     TITLE = {Nevanlinna theory and iteration of rational maps},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {249},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {125--138},
      ISSN = {0025-5874},
     CODEN = {MAZEAX},
   MRCLASS = {11J97 (30D05 30D35 37F10)},
  MRNUMBER = {MR2106974 (2005i:11096)},
MRREVIEWER = {William A. Cherry},
}

@book {MR924157,
    AUTHOR = {Rudin, Walter},
     TITLE = {Real and {C}omplex {A}nalysis},
   EDITION = {Third},
 PUBLISHER = {McGraw-Hill Book Co.},
   ADDRESS = {New York},
      YEAR = {1987},
     PAGES = {xiv+416},
      ISBN = {0-07-054234-1},
   MRCLASS = {00A05 (26-01 30-01 46-01)},
  MRNUMBER = {MR924157 (88k:00002)},
}
@comment{arxiv1304.5601, Nottingham group}
@article {MR3394117,
    AUTHOR = {Ruggiero, Matteo},
     TITLE = {Classification of one-dimensional superattracting germs in
              positive characteristic},
   JOURNAL = {Ergodic Theory Dynam. Systems},
  FJOURNAL = {Ergodic Theory and Dynamical Systems},
    VOLUME = {35},
      YEAR = {2015},
    NUMBER = {7},
     PAGES = {2242--2268},
      ISSN = {0143-3857},
   MRCLASS = {37P10 (37F10 37F50)},
  MRNUMBER = {3394117},
MRREVIEWER = {Mattias Jonsson},
       DOI = {10.1017/etds.2014.35},
       URL = {http://dx.doi.org/10.1017/etds.2014.35},
}
@article {MR3186512,
    AUTHOR = {Ruggiero, Matteo},
     TITLE = {Contracting rigid germs in higher dimensions},
   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier},
    VOLUME = {63},
      YEAR = {2013},
    NUMBER = {5},
     PAGES = {1913--1950},
      ISSN = {0373-0956},
   MRCLASS = {37F25},
  MRNUMBER = {3186512},
MRREVIEWER = {Peter Ha\"\i ssinsky},
       DOI = {10.5802/aif.2818},
       URL = {https://doi.org/10.5802/aif.2818},
}
@comment{arXiv:1304.1201}
@article {MR3361223,
    AUTHOR = {Rumely, Robert},
     TITLE = {The minimal resultant locus},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {169},
      YEAR = {2015},
    NUMBER = {3},
     PAGES = {251--290},
      ISSN = {0065-1036},
   MRCLASS = {37P50 (11S82 37P05)},
  MRNUMBER = {3361223},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.4064/aa169-3-3},
       URL = {http://dx.doi.org/10.4064/aa169-3-3},
}
@comment{UPDATE}
@misc {arxiv1402.6017,
    AUTHOR = {Rumely, Robert},
    TITLE = {The Geometry of the Minimal Resultant Locus},
     YEAR = {2014},
     NOTE = {\url{arXiv:1402.6017}},
}
@article {MR3665639,
    AUTHOR = {Rumely, Robert},
     TITLE = {A new equivariant in nonarchimedean dynamics},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {11},
      YEAR = {2017},
    NUMBER = {4},
     PAGES = {841--884},
      ISSN = {1937-0652},
   MRCLASS = {37P50 (11S82 37P05)},
  MRNUMBER = {3665639},
       URL = {https://doi.org/10.2140/ant.2017.11.841},
}
@article {MR1488341,
    AUTHOR = {Russakovskii, Alexander and Shiffman, Bernard},
     TITLE = {Value distribution for sequences of rational mappings and
              complex dynamics},
   JOURNAL = {Indiana Univ. Math. J.},
  FJOURNAL = {Indiana University Mathematics Journal},
    VOLUME = {46},
      YEAR = {1997},
    NUMBER = {3},
     PAGES = {897--932},
      ISSN = {0022-2518},
     CODEN = {IUMJAB},
   MRCLASS = {32H30 (32H50)},
  MRNUMBER = {1488341 (98h:32046)},
MRREVIEWER = {Jeffrey Diller},
       DOI = {10.1512/iumj.1997.46.1441},
       URL = {http://dx.doi.org/10.1512/iumj.1997.46.1441},
}
@comment{This article defines the various dynamical degrees defined in terms of pull-backs of linear spaces}

@comment{--SSS-- }

@comment{UPDATE}
@misc {arxiv1804.09839,
    AUTHOR = {Sadek, Mohammad},
    TITLE = {On rational periodic points of {$x^d+c$}},
     YEAR = {2018},
     NOTE = {\url{arXiv:1804.09839}},
}
@comment{UPDATE}
@misc {arxiv2010.09910,
    AUTHOR = {Sadek, Mohammad},
    TITLE = {Families of polynomials of every degree with no rational preperiodic points},
     YEAR = {2020},
     NOTE = {\url{arXiv:2010.09910}},
}
@comment{UPDATE}
@misc {arxiv2209.07624,
    AUTHOR = {Sadek, Mohammad and Wafik, Mohamed},
    TITLE = {Construction of polynomials with prescribed divisibility
                  conditions on the critical orbit},
     YEAR = {2022},
     NOTE = {\url{arXiv:2209.07624}},
}
@comment{arxiv1708.09275}
@article {MR4038034,
    AUTHOR = {Salerno, Adriana and Silverman, Joseph H.},
     TITLE = {Integrality properties of {B}\"{o}ttcher coordinates for
              one-dimensional superattracting germs},
   JOURNAL = {Ergodic Theory Dynam. Systems},
  FJOURNAL = {Ergodic Theory and Dynamical Systems},
    VOLUME = {40},
      YEAR = {2020},
    NUMBER = {1},
     PAGES = {248--271},
      ISSN = {0143-3857},
   MRCLASS = {37P05 (11S82)},
  MRNUMBER = {4038034},
       DOI = {10.1017/etds.2018.41},
       URL = {https://doi.org/10.1017/etds.2018.41},
}
@comment{arxiv1604.04174}
@article {MR4079421,
    AUTHOR = {Sano, Kaoru},
     TITLE = {Dynamical degree and arithmetic degree of endomorphisms on
              product varieties},
   JOURNAL = {Tohoku Math. J. (2)},
  FJOURNAL = {The Tohoku Mathematical Journal. Second Series},
    VOLUME = {72},
      YEAR = {2020},
    NUMBER = {1},
     PAGES = {1--13},
      ISSN = {0040-8735},
   MRCLASS = {37P55 (11G50)},
  MRNUMBER = {4079421},
       DOI = {10.2748/tmj/1585101618},
       URL = {https://doi.org/10.2748/tmj/1585101618},
}
@comment{UPDATE}
@misc {arxiv1712.07533,
    AUTHOR = {Sano, Kaoru},
    TITLE = {The canonical heights for {J}ordan blocks of small
                  eigenvalues, preperiodic points, and the arithmetic
                  degrees},
     YEAR = {2017},
     NOTE = {\url{arXiv:1712.07533}},
}
@comment{arxiv1801.02831}
@article {MR3869605,
    AUTHOR = {Sano, Kaoru},
     TITLE = {Growth rate of ample heights and the dynamical
              {M}ordell-{L}ang conjecture},
   JOURNAL = {Int. J. Number Theory},
  FJOURNAL = {International Journal of Number Theory},
    VOLUME = {14},
      YEAR = {2018},
    NUMBER = {10},
     PAGES = {2673--2685},
      ISSN = {1793-0421},
   MRCLASS = {37P55 (11G50)},
  MRNUMBER = {3869605},
       DOI = {10.1142/S1793042118501610},
       URL = {https://doi.org/10.1142/S1793042118501610},
}
@comment{UPDATE}
@misc {arxiv2007.15180,
    AUTHOR = {Sano, Kaoru and Shibata, Takahiro},
    TITLE = {Zariski density of points with maximal arithmetic degree},
     YEAR = {2020},
     NOTE = {\url{arXiv:2007.15180}},
}
@phdthesis{sarkis:thesis, 
   AUTHOR = {Sarkis, Ghassan},
    TITLE = {Formal {G}roups and $p$-adic {D}ynamical {S}ystems},
   SCHOOL = {Brown University},
     YEAR = {2001}
	}
@article {MR2173969,
    AUTHOR = {Sarkis, Ghassan},
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  FJOURNAL = {Journal of Algebra},
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      YEAR = {2005},
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     PAGES = {130--154},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {11S31 (37C99)},
  MRNUMBER = {MR2173969},
MRREVIEWER = {Fran{\c{c}}ois Laubie},
}

@article {MR2651931,
    AUTHOR = {Sarkis, Ghassan},
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  MRNUMBER = {2651931},
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       URL = {http://dx.doi.org/10.1112/blms/bdp130},
}
@article {MR3063836,
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  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
    VOLUME = {25},
      YEAR = {2013},
    NUMBER = {1},
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      ISSN = {1246-7405},
   MRCLASS = {37P20},
  MRNUMBER = {3063836},
       URL = {http://jtnb.cedram.org/item?id=JTNB_2013__25_1_163_0},
}
@article {MR3305243,
    AUTHOR = {Sattarov, I. A.},
     TITLE = {{$p$}-adic {$(3,2)$}-rational dynamical systems},
   JOURNAL = {p-Adic Numbers Ultrametric Anal. Appl.},
  FJOURNAL = {p-Adic Numbers, Ultrametric Analysis, and Applications},
    VOLUME = {7},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {39--55},
      ISSN = {2070-0466},
   MRCLASS = {37P05},
  MRNUMBER = {3305243},
       DOI = {10.1134/S2070046615010045},
       URL = {http://dx.doi.org/10.1134/S2070046615010045},
}
@comment{UPDATE}
@misc {arxiv:0807.4162,
    AUTHOR = {Scanlon, Thomas},
    TITLE = {Analytic relations on a dynamical orbit},
     YEAR = {2008},
     NOTE = {\url{arXiv:0807.4162}},
}

@comment{arxiv1212.1836}
@article {MR3250036,
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    NUMBER = {16},
     PAGES = {4357--4367},
      ISSN = {1073-7928},
   MRCLASS = {37P05 (11C08 20G30)},
  MRNUMBER = {3250036},
}
@book {MR2700328,
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@article{schanuel:heights, 
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@PHDTHESIS{schleicherphd94,
  AUTHOR = {Schleicher, Dierk},
 TITLE   = {Internal addresses in the {M}andelbrot set and irreducibility of polynomials},
 SCHOOL  = {Cornell University},
 ADDRESS = {Ithaca NY},
 YEAR    = {1994},
}
@article {MR3646529,
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   MRCLASS = {37F20 (12F10 30D05 37E15 37F10 37F45)},
  MRNUMBER = {3646529},
       URL = {https://doi.org/10.1007/s40598-016-0042-x},
      NOTE = {rewritten and updated version of Stony Brook IMS 1994/19},
}
@comment{UPDATE}
@misc {arxiv2009.07609,
    AUTHOR = {Schmidt, Harry},
    TITLE = {Polynomial dynamics and local analysis},
     YEAR = {2020},
     NOTE = {\url{arXiv:2009.07609}},
}
@article {MR1328699,
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   JOURNAL = {Bull. London Math. Soc.},
  FJOURNAL = {The Bulletin of the London Mathematical Society},
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     CODEN = {LMSBBT},
   MRCLASS = {30D05},
  MRNUMBER = {MR1328699 (96e:30061)},
MRREVIEWER = {Lo Yang},
}
@comment{For any Julia set (of a polynomial) $J$ which is neither a
circle nor a straight line segment, there exists a polynomial $P$ such
that any polynomial with Julia set $J$ can be written in the form
$\sigma P^n$, where $\sigma$ is a rotation mapping $J$ onto itself,
and $n$ is a positive integer.}

@book {MR568710,
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 PUBLISHER = {Springer},
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     PAGES = {x+299},
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   MRCLASS = {10Fxx (10-02)},
  MRNUMBER = {MR568710 (81j:10038)},
MRREVIEWER = {A. J. van der Poorten},
}

@book{schmidt:algebraicdynamics, 
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 PUBLISHER = {Birkh\"auser Verlag},
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  MRNUMBER = {MR1345152 (97c:28041)},
MRREVIEWER = {Mahesh Nerurkar},
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@article {MR3711376,
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@article {MR1297061,
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@incollection {MR1136071,
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}
@comment{UPDATE}
@misc {arxiv1502.06923,
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    TITLE = {Dynamics on supersingular {K3} surfaces},
     YEAR = {2015},
     NOTE = {\url{arXiv:1502.06923}},
}
@incollection {MR2732092,
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@article {MR2135559,
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@book {MR554237,
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@book {MR0450380,
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@book {MR1757192,
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@book {MR1484415,
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@article {MR0387283,
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@book {MR0201468,
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@article {arxiv1101.3482,
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@article{arxiv0910.5550,
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}
@comment{UPDATE}
@misc {arxiv2106.07745,
    AUTHOR = {Shaikh, Absos Ali and Sarkar, Mabud Ali},
    TITLE = {Rigidity and unlikely intersections for stable $p$-adic dynamical systems},
     YEAR = {2021},
     NOTE = {\url{arXiv:2106.07745}},
}
@comment{UPDATE}
@misc {arxiv2001.11726,
    AUTHOR = {Shalit, Ehud de},
    TITLE = {Criteria for periodicity and an application to elliptic functions},
     YEAR = {2020},
     NOTE = {\url{arXiv:2001.11726}},
}
@comment{UPDATE}
@misc {arxiv1302.2324,
    AUTHOR = {Shankar, B. R. and Palimar, Sushma},
    TITLE = {Hensel's Lemma, Backward Dynamics and $p$-adic Approximations},
     YEAR = {2013},
     NOTE = {\url{arXiv:1302.2324}},
}
@article {MR3437764,
    AUTHOR = {Shao, Xuancheng},
     TITLE = {Polynomial values modulo primes on average and sharpness of
              the larger sieve},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {9},
      YEAR = {2015},
    NUMBER = {10},
     PAGES = {2325--2346},
      ISSN = {1937-0652},
   MRCLASS = {11N05 (11N35 11R09 11R45 11R47 11T06)},
  MRNUMBER = {3437764},
MRREVIEWER = {Jan-Christoph Schlage-Puchta},
       DOI = {10.2140/ant.2015.9.2325},
       URL = {https://doi.org/10.2140/ant.2015.9.2325},
}
@comment{UPDATE}
@misc {arxiv1710.05278,
    AUTHOR = {Shibata, Takahiro},
    TITLE = {Ample canonical heights for endomorphisms on projective varieties},
     YEAR = {2017},
     NOTE = {\url{arXiv:1710.05278}},
}
@article {shimura:fldofdef,
   AUTHOR = {Shimura, Goro},
    TITLE = {On the field of definition for a field of automorphic
             functions. {I}, {I}{I}, {I}{I}{I}},
  JOURNAL = {Ann. of Math. (2)},
   VOLUME = {80, 81, 83},
     YEAR = {1964, 1965, 1966},
    PAGES = {160--189, 124--165, 377--385},
}
@book {MR0125113,
    AUTHOR = {Shimura, Goro and Taniyama, Yutaka},
     TITLE = {Complex multiplication of abelian varieties and its
              applications to number theory},
    SERIES = {Publications of the Mathematical Society of Japan},
    VOLUME = {6},
 PUBLISHER = {The Mathematical Society of Japan, Tokyo},
      YEAR = {1961},
     PAGES = {xi+159},
   MRCLASS = {14.40 (10.68)},
  MRNUMBER = {0125113},
MRREVIEWER = {I. Barsotti},
}
@book {MR1291394,
    AUTHOR = {Shimura, Goro},
     TITLE = {Introduction to the {A}rithmetic {T}heory of {A}utomorphic
              {F}unctions},
    SERIES = {Publications of the Mathematical Society of Japan},
    VOLUME = {11},
      NOTE = {Reprint of the 1971 original,
              Kan\^o Memorial Lectures, 1},
 PUBLISHER = {Princeton University Press},
   ADDRESS = {Princeton, NJ},
      YEAR = {1994},
     PAGES = {xiv+271},
      ISBN = {0-691-08092-5},
   MRCLASS = {11Fxx (11-02 11G05 11G40)},
  MRNUMBER = {MR1291394 (95e:11048)},
}
@article {MR892140,
    AUTHOR = {Shishikura, Mitsuhiro},
     TITLE = {On the quasiconformal surgery of rational functions},
   JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
  FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. Quatri\`eme
              S\'erie},
    VOLUME = {20},
      YEAR = {1987},
    NUMBER = {1},
     PAGES = {1--29},
      ISSN = {0012-9593},
   MRCLASS = {58F11 (30D05 58F20)},
  MRNUMBER = {892140},
MRREVIEWER = {Robert L. Devaney},
       URL = {http://www.numdam.org/item?id=ASENS_1987_4_20_1_1_0},
}
	
@article {MR917803,
    AUTHOR = {Shparlinski{\u\i}, I. E.},
     TITLE = {The number of different prime divisors of recurrent sequences},
   JOURNAL = {Mat. Zametki},
  FJOURNAL = {Akademiya Nauk {S}{S}{S}{R}. Matematicheskie Zametki},
    VOLUME = {42},
      YEAR = {1987},
    NUMBER = {4},
     PAGES = {494--507, 622},
      ISSN = {0025-567X},
   MRCLASS = {11N99 (11B37)},
  MRNUMBER = {MR917803 (89k:11092)},
MRREVIEWER = {Grigori Kolesnik},
}
@article {arxiv0607779,
    AUTHOR = {Shparlinski, Igor},
    TITLE = {On Some Dynamical Systems in Finite Fields and Residue Rings},
   JOURNAL = {Discrete Contin. Dyn. Syst.},
  FJOURNAL = {Discrete and Continuous Dynamical Systems. Series A},
    VOLUME = {17},
      YEAR = {2007},
     PAGES = {901--917},
}
@article {MR3784060,
    AUTHOR = {Shparlinski, Igor E.},
     TITLE = {MULTIPLICATIVE ORDERS IN ORBITS OF POLYNOMIALS
              OVER FINITE FIELDS},
   JOURNAL = {Glasg. Math. J.},
  FJOURNAL = {Glasgow Mathematical Journal},
    VOLUME = {60},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {487--493},
      ISSN = {0017-0895},
   MRCLASS = {11T06 (37P05 37P25)},
  MRNUMBER = {3784060},
       DOI = {10.1017/S0017089517000222},
       URL = {https://doi.org/10.1017/S0017089517000222},
}
@article {MR4080881,
    AUTHOR = {Shparlinski, Igor E.},
     TITLE = {Orders of points in families of elliptic curves},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {148},
      YEAR = {2020},
    NUMBER = {6},
     PAGES = {2371--2377},
      ISSN = {0002-9939},
   MRCLASS = {11G05 (11G07)},
  MRNUMBER = {4080881},
       DOI = {10.1090/proc/14901},
       URL = {https://doi.org/10.1090/proc/14901},
}
			
@incollection {sibony:panoramas,
    AUTHOR = {Sibony, Nessim},
     TITLE = {Dynamique des applications rationnelles de {$\mathbb{P}\sp k$}},
 BOOKTITLE = {Dynamique et g\'eom\'etrie complexes (Lyon, 1997)},
    SERIES = {Panor. Synth\`eses},
    VOLUME = {8},
     PAGES = {ix--x, xi--xii, 97--185},
 PUBLISHER = {Soc. Math. France},
   ADDRESS = {Paris},
      YEAR = {1999},
   MRCLASS = {32H50 (37F10 37F50)},
  MRNUMBER = {MR1760844 (2001e:32026)},
MRREVIEWER = {Mattias Jonsson},
}

@incollection {MR2052279,
    AUTHOR = {Sidorov, Nikita},
     TITLE = {Arithmetic dynamics},
 BOOKTITLE = {Topics in Dynamics and Ergodic Theory},
    SERIES = {London Math. Soc. Lecture Note Ser.},
    VOLUME = {310},
     PAGES = {145--189},
 PUBLISHER = {Cambridge Univ. Press},
   ADDRESS = {Cambridge},
      YEAR = {2003},
   MRCLASS = {37B10 (11K16 37A45)},
  MRNUMBER = {MR2052279},
MRREVIEWER = {Manfred Einsiedler},
}
@comment{From MR: In this survey paper the author describes a collection of
results dealing with arithmetic expansions of various dynamical
systems---a (to be developed) branch of symbolic dynamics the author
calls arithmetic dynamics.}

@article{siegel:hyperellipticintegerpoints, 
   AUTHOR = {Siegel, C.L.},
    TITLE = {The integer solutions of the equation $y^2=ax^n+bx^{n-1}+\cdots+k$},
  JOURNAL = {J. London Math. Soc.},
   VOLUME = {1},
     YEAR = {1926},
    PAGES = {66--68}
}

@incollection {siegeldiophappr,
   AUTHOR = {Siegel, C.L.},
     TITLE = {{\"U}ber einige {A}nwendungen diophantischer {A}pproximationen},
 BOOKTITLE = {Collected Works},
     PAGES = {209--266},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1966},
}
@book {MR1020761,
    AUTHOR = {Siegel, Carl Ludwig},
     TITLE = {Lectures on the geometry of numbers},
      NOTE = {Notes by B. Friedman,
              Rewritten by Komaravolu Chandrasekharan with the assistance of
              Rudolf Suter,
              With a preface by Chandrasekharan},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1989},
     PAGES = {x+160},
      ISBN = {3-540-50629-2},
   MRCLASS = {11Hxx (01A75)},
  MRNUMBER = {1020761},
MRREVIEWER = {Rudolf Scharlau},
       DOI = {10.1007/978-3-662-08287-4},
       URL = {https://doi.org/10.1007/978-3-662-08287-4},
}
@article {MR3582054,
    AUTHOR = {Sijsling, Jeroen and Voight, John},
     TITLE = {On explicit descent of marked curves and maps},
   JOURNAL = {Res. Number Theory},
  FJOURNAL = {Research in Number Theory},
    VOLUME = {2},
      YEAR = {2016},
     PAGES = {Art. 27, 35},
      ISSN = {2363-9555},
   MRCLASS = {14H30 (11G05 14H25)},
  MRNUMBER = {3582054},
MRREVIEWER = {Remke Kloosterman},
       DOI = {10.1007/s40993-016-0057-3},
       URL = {https://doi.org/10.1007/s40993-016-0057-3},
}
@book {MR817210,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {The {A}rithmetic of {E}lliptic {C}urves},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {106},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {1986},
     PAGES = {xii+400},
      ISBN = {0-387-96203-4},
   MRCLASS = {11G05 (14Gxx 14K07 14K15)},
  MRNUMBER = {817210},
MRREVIEWER = {Robert S. Rumely},
       DOI = {10.1007/978-1-4757-1920-8},
       URL = {http://dx.doi.org/10.1007/978-1-4757-1920-8},
}
@book{silverman:aec, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {The {A}rithmetic of {E}lliptic {C}urves},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {106},
      NOTE = {Corrected reprint of the 1986 original},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1992},
     PAGES = {xii+400},
      ISBN = {0-387-96203-4},
   MRCLASS = {11G05 (14H52)},
  MRNUMBER = {MR1329092 (95m:11054)},
}
@book {MR2514094,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {The {A}rithmetic of {E}lliptic {C}urves},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {106},
   EDITION = {Second},
 PUBLISHER = {Springer},
   ADDRESS = {Dordrecht},
      YEAR = {2009},
     PAGES = {xx+513},
      ISBN = {978-0-387-09493-9},
   MRCLASS = {11-02 (11G05 14Gxx 14Kxx 14K15)},
  MRNUMBER = {MR2514094},
       DOI = {10.1007/978-0-387-09494-6},
       URL = {http://dx.doi.org/10.1007/978-0-387-09494-6},
}

@book{silverman:ataec, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Advanced {T}opics in the {A}rithmetic of {E}lliptic {C}urves},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {151},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1994},
     PAGES = {xiv+525},
      ISBN = {0-387-94328-5},
   MRCLASS = {11G05 (11G07 11G15 11G40 14H52)},
  MRNUMBER = {MR1312368 (96b:11074)},
MRREVIEWER = {Henri Darmon},
}
@book {MR2316407,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {The {A}rithmetic of {D}ynamical {S}ystems},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {241},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2007},
     PAGES = {x+511},
      ISBN = {978-0-387-69903-5},
   MRCLASS = {11-01 (11G99 37Bxx 37Fxx)},
  MRNUMBER = {MR2316407},
}
@article {silverman:K3htseries,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {A zeta function over a recurrent sequence},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {106},
      YEAR = {1999},
    NUMBER = {7},
     PAGES = {686--688},
      NOTE = {Problem 10486 with solutions},
}
@book {MR2632102,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {The N{\'e}ron--Tate height on elliptic curves},
      NOTE = {Thesis (Ph.D.)--Harvard University},
 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {1982},
     PAGES = {62},
   MRCLASS = {Thesis},
  MRNUMBER = {2632102},
}
@article {MR747871,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Lower bounds for height functions},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {51},
      YEAR = {1984},
    NUMBER = {2},
     PAGES = {395--403},
      ISSN = {0012-7094},
   MRCLASS = {11G10 (11G05 14G25 14K15)},
  MRNUMBER = {747871},
MRREVIEWER = {J. Top},
       URL = {https://doi.org/10.1215/S0012-7094-84-05118-4},
}
@article {MR2029512,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {A lower bound for the canonical height on elliptic curves over
              abelian extensions},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {104},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {353--372},
      ISSN = {0022-314X},
   MRCLASS = {11G50 (11G05 11G10 14G25 14K15)},
  MRNUMBER = {2029512},
MRREVIEWER = {Robin de Jong},
       DOI = {10.1016/j.jnt.2003.07.001},
       URL = {https://doi.org/10.1016/j.jnt.2003.07.001},
}
@article {silverman:integerpointsongenus1,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Integer points on curves of genus {$1$}},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {The Journal of the London Mathematical Society. Second Series},
    VOLUME = {28},
      YEAR = {1983},
    NUMBER = {1},
     PAGES = {1--7},
      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {10B10 (10J06 14G25 14K15)},
  MRNUMBER = {MR703458 (84g:10033)},
MRREVIEWER = {Michael Laska},
}
@article {MR703488,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Heights and the specialization map for families of abelian
              varieties},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {342},
      YEAR = {1983},
     PAGES = {197--211},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {14K15 (14D10 14G25)},
  MRNUMBER = {MR703488 (84k:14033)},
MRREVIEWER = {Gerd Faltings},
}
@article {MR895285,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {A quantitative version of {S}iegel's theorem: integral points
              on elliptic curves and {C}atalan curves},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {378},
      YEAR = {1987},
     PAGES = {60--100},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11G05 (14G25)},
  MRNUMBER = {MR895285 (89g:11047)},
MRREVIEWER = {Toshihiro Hadano},
}
@book {MR1171452,
    AUTHOR = {Silverman, Joseph H. and Tate, John},
     TITLE = {Rational {P}oints on {E}lliptic {C}urves},
    SERIES = {Undergraduate Texts in Mathematics},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1992},
     PAGES = {x+281},
      ISBN = {0-387-97825-9},
   MRCLASS = {11-01 (11D25 11G05 14H52)},
  MRNUMBER = {MR1171452 (93g:11003)},
MRREVIEWER = {Andrew Bremner},
}
@book {MR3363545,
    AUTHOR = {Silverman, Joseph H. and Tate, John T.},
     TITLE = {Rational {P}oints on {E}lliptic {C}urves},
    SERIES = {Undergraduate Texts in Mathematics},
   EDITION = {Second},
 PUBLISHER = {Springer, Cham},
      YEAR = {2015},
     PAGES = {xxii+332},
      ISBN = {978-3-319-18587-3; 978-3-319-18588-0},
   MRCLASS = {11-01 (11D25 11G05 14G05 14H52)},
  MRNUMBER = {3363545},
       DOI = {10.1007/978-3-319-18588-0},
       URL = {http://dx.doi.org/10.1007/978-3-319-18588-0},
}
@article{silverman:computecanonicalht,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Computing heights on elliptic curves},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {51},
      YEAR = {1988},
    NUMBER = {183},
     PAGES = {339--358},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {11G05 (11D25 11Y40 14G25 14K15)},
  MRNUMBER = {MR942161 (89d:11049)},
MRREVIEWER = {Philippe Satg{\'e}},
}
@article {MR1035944,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {The difference between the {W}eil height and the canonical
              height on elliptic curves},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {55},
      YEAR = {1990},
    NUMBER = {192},
     PAGES = {723--743},
      ISSN = {0025-5718},
   MRCLASS = {11G05 (14G25)},
  MRNUMBER = {1035944},
MRREVIEWER = {Marc Hindry},
       DOI = {10.2307/2008444},
       URL = {https://doi.org/10.2307/2008444},
}
@article {MR961918,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Wieferich's criterion and the {$abc$}-conjecture},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {30},
      YEAR = {1988},
    NUMBER = {2},
     PAGES = {226--237},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11D41 (11G05)},
  MRNUMBER = {961918 (89m:11027)},
MRREVIEWER = {Daniel Bertrand},
       DOI = {10.1016/0022-314X(88)90019-4},
       URL = {http://dx.doi.org/10.1016/0022-314X(88)90019-4},
}

@article{silverman:K3heights, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Rational points on {K3} surfaces: a new canonical height},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {105},
      YEAR = {1991},
    NUMBER = {2},
     PAGES = {347--373},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14G05 (11G35 14J20 14J28)},
  MRNUMBER = {MR1115546 (92k:14025)},
MRREVIEWER = {I. Dolgachev},
}

@article{silverman:dynamicalintegerpoints, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Integer points, {D}iophantine approximation, and iteration of
              rational maps},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {71},
      YEAR = {1993},
    NUMBER = {3},
     PAGES = {793--829},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {11G99 (11J99)},
  MRNUMBER = {MR1240603 (95e:11070)},
MRREVIEWER = {Jeffrey Lin Thunder},
}

@article{silverman:henonmap, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Geometric and arithmetic properties of the {H}\'enon map},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {215},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {237--250},
      ISSN = {0025-5874},
     CODEN = {MAZEAX},
   MRCLASS = {14G25 (11G99 14E05 58F20)},
  MRNUMBER = {MR1259460 (95f:14040)},
MRREVIEWER = {Takeshi Ooe},
}

@article{silverman:fieldofdef, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {The field of definition for dynamical systems on {$\mathbb{P}\sp 1$}},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {98},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {269--304},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11G99 (11R27 14E22)},
  MRNUMBER = {MR1351830 (96j:11090)},
MRREVIEWER = {Laurent Denis},
}

@article{silverman:polynomialiterate, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Rational functions with a polynomial iterate},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {180},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {102--110},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {11G99},
  MRNUMBER = {MR1375568 (96j:11091)},
MRREVIEWER = {Jeffrey Lin Thunder},
}
@article {MR1388892,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Computing canonical heights with little (or no) factorization},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {66},
      YEAR = {1997},
    NUMBER = {218},
     PAGES = {787--805},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {11G05 (11Y16)},
  MRNUMBER = {MR1388892 (97f:11040)},
MRREVIEWER = {Alain Kraus},
}

@article{silverman:modulirationalmaps, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {The space of rational maps on {$\mathbb{P}\sp 1$}},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {94},
      YEAR = {1998},
    NUMBER = {1},
     PAGES = {41--77},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {14D10 (14L30 26A18 37E99 37F10)},
  MRNUMBER = {MR1635900 (2000m:14010)},
}

@article{silverman:arithdistfunctions, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Arithmetic distance functions and height functions in
              {D}iophantine geometry},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {279},
      YEAR = {1987},
    NUMBER = {2},
     PAGES = {193--216},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {11G99 (11D99 14G99)},
  MRNUMBER = {MR919501 (89a:11066)},
MRREVIEWER = {Andrew Bremner},
}
@article {MR2162351,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Generalized greatest common divisors, divisibility sequences,
              and {V}ojta's conjecture for blowups},
   JOURNAL = {Monatsh. Math.},
  FJOURNAL = {Monatshefte f\"ur Mathematik},
    VOLUME = {145},
      YEAR = {2005},
    NUMBER = {4},
     PAGES = {333--350},
      ISSN = {0026-9255},
     CODEN = {MNMTA2},
   MRCLASS = {11G35 (11D75 11J25 14G25)},
  MRNUMBER = {2162351 (2006e:11087)},
MRREVIEWER = {Yann Bugeaud},
       DOI = {10.1007/s00605-005-0299-y},
       URL = {http://dx.doi.org/10.1007/s00605-005-0299-y},
}

@article {silverman:htregauts,
    AUTHOR = {Silverman, Joseph H.},
    TITLE = {Height Bounds and Preperiodic Points  for 
         Families of Jointly Regular Affine Maps},
   JOURNAL = {Quart. J. Pure Appl. Math.},
    VOLUME = {2},
      YEAR = {2006},
     PAGES = {135--145},
}

@article {arXiv:0707.1505,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Variation of periods modulo {$p$} in arithmetic dynamics},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {14},
      YEAR = {2008},
     PAGES = {601--616},
      ISSN = {1076-9803},
   MRCLASS = {11G35 (11G50 11R45 14G40 37F10)},
  MRNUMBER = {MR2448661},
MRREVIEWER = {Thomas Ward},
}
@article {arxiv0908.3835,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Height estimates for equidimensional dominant rational maps},
   JOURNAL = {J. Ramanujan Math. Soc.},
  FJOURNAL = {Journal of the Ramanujan Mathematical Society},
    VOLUME = {26},
      YEAR = {2011},
    NUMBER = {2},
     PAGES = {145--163},
      ISSN = {0970-1249},
   MRCLASS = {11G50 (14G40 37P30)},
  MRNUMBER = {2816785 (2012f:11122)},
MRREVIEWER = {Thomas Ward},
}
@comment{MR2929011}
@article {arxiv1010.4562,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {An algebraic approach to certain cases of {T}hurston rigidity},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {140},
      YEAR = {2012},
    NUMBER = {10},
     PAGES = {3421--3434},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {37-XX},
  MRNUMBER = {2929011},
       DOI = {10.1090/S0002-9939-2012-11171-2},
       URL = {http://dx.doi.org/10.1090/S0002-9939-2012-11171-2},
}
@article {MR3057058,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Primitive divisors, dynamical {Z}sigmondy sets, and {V}ojta's
              conjecture},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {133},
      YEAR = {2013},
    NUMBER = {9},
     PAGES = {2948--2963},
      ISSN = {0022-314X},
   MRCLASS = {37P15 (11B50 11G35 11J97 37P55)},
  MRNUMBER = {3057058},
MRREVIEWER = {Andreas O. Bender},
       URL = {https://doi.org/10.1016/j.jnt.2013.03.005},
}
@article {MR3113229,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {What is{$\dots$}the {$p$}-adic {M}andelbrot set?},
   JOURNAL = {Notices Amer. Math. Soc.},
  FJOURNAL = {Notices of the American Mathematical Society},
    VOLUME = {60},
      YEAR = {2013},
    NUMBER = {8},
     PAGES = {1048--1050},
      ISSN = {0002-9920},
   MRCLASS = {28-01},
  MRNUMBER = {3113229},
MRREVIEWER = {Vasileios Drakopoulos},
       DOI = {10.1090/noti1038},
       URL = {https://doi.org/10.1090/noti1038},
}
		
@article {arxiv1111.5664,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Dynamical degree, arithmetic entropy, and canonical heights
              for dominant rational self-maps of projective space},
   JOURNAL = {Ergodic Theory Dynam. Systems},
  FJOURNAL = {Ergodic Theory and Dynamical Systems},
    VOLUME = {34},
      YEAR = {2014},
    NUMBER = {2},
     PAGES = {647--678},
      ISSN = {0143-3857},
   MRCLASS = {37F45 (14E05 37B40)},
  MRNUMBER = {3233709},
       DOI = {10.1017/etds.2012.144},
}
@book {MR2884382,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Moduli {S}paces and {A}rithmetic {D}ynamics},
    SERIES = {CRM Monograph Series},
    VOLUME = {30},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2012},
     PAGES = {viii+140},
      ISBN = {978-0-8218-7582-7},
   MRCLASS = {37Pxx},
  MRNUMBER = {2884382},
}
@comment{arxiv1609.02119}
@article {MR3841148,
    AUTHOR = {Silverman, Joseph H. and Call, Gregory S.},
     TITLE = {Degeneration of dynamical degrees in families of maps},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {184},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {101--116},
      ISSN = {0065-1036},
   MRCLASS = {37P05 (11G50 37P30 37P55)},
  MRNUMBER = {3841148},
       DOI = {10.4064/aa8620-5-2017},
       URL = {https://doi.org/10.4064/aa8620-5-2017},
}

@comment{arxiv1501.04205}
@article {MR3614521,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Arithmetic and dynamical degrees on abelian varieties},
   JOURNAL = {J. Th\'eor. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
    VOLUME = {29},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {151--167},
      ISSN = {1246-7405},
   MRCLASS = {37P30 (11G10 11G50 37P15)},
  MRNUMBER = {3614521},
       URL = {http://jtnb.cedram.org/item?id=JTNB_2017__29_1_151_0},
}
@article {MR3630720,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Divisor divisibility sequences on tori},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {177},
      YEAR = {2017},
    NUMBER = {4},
     PAGES = {315--345},
      ISSN = {0065-1036},
   MRCLASS = {14G25 (11B39 14L10)},
  MRNUMBER = {3630720},
MRREVIEWER = {Patrick Ingram},
       DOI = {10.4064/aa8381-11-2016},
       URL = {https://doi.org/10.4064/aa8381-11-2016},
}
@article {arxiv1703.00823,
    AUTHOR = {Silverman, Joseph},
     TITLE = {Good reduction and {S}hafarevich-type theorems for dynamical
              systems with portrait level structures},
   JOURNAL = {Pacific J. Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {295},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {145--190},
      ISSN = {0030-8730},
   MRCLASS = {37P45 (37P15)},
  MRNUMBER = {3778330},
       DOI = {10.2140/pjm.2018.295.145},
       URL = {https://doi.org/10.2140/pjm.2018.295.145},
}
@comment{MR3162847}
@article {arxiv1109.0207,
    AUTHOR = {Silverman, Joseph H. and Viray, Bianca},
     TITLE = {On a uniform bound for the number of exceptional linear
              subvarieties in the dynamical {M}ordell-{L}ang conjecture},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {20},
      YEAR = {2013},
    NUMBER = {3},
     PAGES = {547--566},
      ISSN = {1073-2780},
   MRCLASS = {37P15 (11D45 37P05)},
  MRNUMBER = {3162847},
       DOI = {10.4310/MRL.2013.v20.n3.a12},
}


@article {MR2226354,
    AUTHOR = {Silverman, Joseph H. and Stephens, Nelson},
     TITLE = {The sign of an elliptic divisibility sequence},
   JOURNAL = {J. Ramanujan Math. Soc.},
  FJOURNAL = {Journal of the Ramanujan Mathematical Society},
    VOLUME = {21},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {1--17},
      ISSN = {0970-1249},
   MRCLASS = {11G05 (11B83)},
  MRNUMBER = {MR2226354 (2007a:11075)},
MRREVIEWER = {Manfred Einsiedler},
}

@article {MR2496466,
    AUTHOR = {Silverman, Joseph H. and Voloch, Jos{\'e} Felipe},
     TITLE = {A local-global criterion for dynamics on {$\mathbb{P}^1$}},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {137},
      YEAR = {2009},
    NUMBER = {3},
     PAGES = {285--294},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11B37 (11G99 14Gxx 37Fxx)},
  MRNUMBER = {MR2496466},
       DOI = {10.4064/aa137-3-8},
       URL = {http://dx.doi.org/10.4064/aa137-3-8},
}
@comment{UPDATE}
@misc {arxiv1712.01372,
    AUTHOR = {Silverman, Thomas},
    TITLE = {A non-archimedean $\lambda$-lemma},
     YEAR = {2017},
     NOTE = {\url{arXiv:1712.01372}},
}
@article{smyth:lehmer, 
    AUTHOR = {Smyth, C. J.},
     TITLE = {On the product of the conjugates outside the unit circle of an
              algebraic integer},
   JOURNAL = {Bull. London Math. Soc.},
  FJOURNAL = {The Bulletin of the London Mathematical Society},
    VOLUME = {3},
      YEAR = {1971},
     PAGES = {169--175},
      ISSN = {0024-6093},
   MRCLASS = {10.65},
  MRNUMBER = {MR0289451 (44 \#6641)},
MRREVIEWER = {H. W. Brinkmann},
}
@article {MR615132,
    AUTHOR = {Smyth, C. J.},
     TITLE = {On measures of polynomials in several variables},
   JOURNAL = {Bull. Austral. Math. Soc.},
  FJOURNAL = {Bulletin of the Australian Mathematical Society},
    VOLUME = {23},
      YEAR = {1981},
    NUMBER = {1},
     PAGES = {49--63},
      ISSN = {0004-9727},
     CODEN = {ALNBAB},
   MRCLASS = {10K50 (12A15)},
  MRNUMBER = {615132 (82k:10074)},
MRREVIEWER = {G{\'e}rard Rauzy},
       DOI = {10.1017/S0004972700006894},
       URL = {http://dx.doi.org/10.1017/S0004972700006894},
}
@incollection  {arxiv0701397,
    AUTHOR = {Smyth, Chris},
     TITLE = {The {M}ahler measure of algebraic numbers: a survey},
 BOOKTITLE = {Number theory and polynomials},
    SERIES = {London Math. Soc. Lecture Note Ser.},
    VOLUME = {352},
     PAGES = {322--349},
 PUBLISHER = {Cambridge Univ. Press},
   ADDRESS = {Cambridge},
      YEAR = {2008},
   MRCLASS = {11R06},
  MRNUMBER = {MR2428530},
}

@comment{arxiv:0808.2679}
@article {MR2782838,
    AUTHOR = {Sookdeo, Vijay A.},
     TITLE = {Integer points in backward orbits},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {131},
      YEAR = {2011},
    NUMBER = {7},
     PAGES = {1229--1239},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {37Pxx (11B37)},
  MRNUMBER = {2782838},
       DOI = {10.1016/j.jnt.2011.01.005},
       URL = {http://dx.doi.org/10.1016/j.jnt.2011.01.005},
}
@comment{UPDATE}
@misc {arxiv1405.1952,
    AUTHOR = {Sookdeo, Vijay A.},
    TITLE = {Backward Orbit Conjecture for {L}att{\`e}s Maps},
     YEAR = {2014},
     NOTE = {\url{arXiv:1405.1952}},
}
@comment{UPDATE}
@misc {arxiv1508.06023,
    AUTHOR = {Sookdeo, Vijay A.},
    TITLE = {Backward Orbit Conjecture for the Powering Map over
                  Global Fields},
     YEAR = {2015},
     NOTE = {\url{arXiv:1508.06023}},
}
@comment{UPDATE}
@misc {arxiv1501.04611,
    AUTHOR = {Specter, Joel},
    TITLE = {The crystalline period of a height one {$p$}-adic dynamical
                  system over {$\mathbf{Z}_p$}},
     YEAR = {2015},
     NOTE = {\url{arXiv:1501.04611}},
}
@comment{UPDATE}
@misc {arxiv1803.00434,
    AUTHOR = {Specter, Joel},
    TITLE = {Polynomials with Surjective Arboreal {G}alois Representations Exist in Every Degree},
     YEAR = {2018},
     NOTE = {\url{arXiv:1803.00434}},
}

@comment{https://repository.library.brown.edu/studio/item/bdr:11323/}
@phdthesis{spencer:thesis, 
    AUTHOR = {Spencer, Matthew P.}, 
    TITLE = {Moduli Spaces of Power Series in Finite Characteristic}, 
   SCHOOL = {Brown University},
     YEAR = {2011},
}    
@misc {speyerMO981,
    AUTHOR = {Speyer, David},
    TITLE = {Rational maps with all critical points fixed},
     YEAR = {2008},
     NOTE = {\url{mathoverflow.net/questions/981/}},
}

@MISC {MO4983,    
    TITLE = {Rational maps with all critical points fixed},    
    AUTHOR = {David Speyer\phantom{x}(mathoverflow.net/users/297)},    
    HOWPUBLISHED = {MathOverflow},    
    NOTE = {\url{mathoverflow.net/questions/4983}},    
}

@book {MR1746847,
    AUTHOR = {Starkov, Alexander N.},
     TITLE = {Dynamical systems on homogeneous spaces},
    SERIES = {Translations of Mathematical Monographs},
    VOLUME = {190},
      NOTE = {Translated from the 1999 Russian original by the author},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2000},
     PAGES = {xvi+243},
      ISBN = {0-8218-1389-7},
   MRCLASS = {37A25 (11E04 11H55 22E40 37C85)},
  MRNUMBER = {MR1746847 (2001m:37013b)},
MRREVIEWER = {S. G. Dani},
}
@comment{UPDATE}
@misc {arxiv0305432,
    AUTHOR = {Starr, Jason},
    TITLE = {The {K}odaira dimension of spaces of rational curves on
             low degree hypersurfaces},
     YEAR = {2003},
     NOTE = {\url{arxiv.org/abs/math/0305432}},
}

@article {MR0398993,
    AUTHOR = {Stewart, C. L.},
     TITLE = {The greatest prime factor of {$a^{n}-b^{n}$}},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Polska Akademia Nauk. Instytut Matematyczny. Acta Arithmetica},
    VOLUME = {26},
      YEAR = {1974/75},
    NUMBER = {4},
     PAGES = {427--433},
      ISSN = {0065-1036},
   MRCLASS = {10F05},
  MRNUMBER = {0398993 (53 \#2844)},
MRREVIEWER = {A. L. Schmidt},
}
@article {MR507748,
    AUTHOR = {Stewart, Cameron L.},
     TITLE = {Algebraic integers whose conjugates lie near the unit circle},
   JOURNAL = {Bull. Soc. Math. France},
  FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France},
    VOLUME = {106},
      YEAR = {1978},
    NUMBER = {2},
     PAGES = {169--176},
      ISSN = {0037-9484},
     CODEN = {BSMFAA},
   MRCLASS = {12A10 (10F40)},
  MRNUMBER = {MR507748 (80a:12002)},
MRREVIEWER = {Christopher Smyth},
}
@misc {arxiv1912.05893,
    AUTHOR = {Stoll, Michael},
    TITLE = {An application of ``{S}elmer group {C}habauty'' to arithmetic dynamics},
     YEAR = {2019},
     NOTE = {\url{arXiv:1912.05893}},
}

@article {MR1174401,
    AUTHOR = {Stoll, Michael},
     TITLE = {Galois groups over {$\mathbb{Q}$} of some iterated polynomials},
   JOURNAL = {Arch. Math. (Basel)},
  FJOURNAL = {Archiv der Mathematik},
    VOLUME = {59},
      YEAR = {1992},
    NUMBER = {3},
     PAGES = {239--244},
      ISSN = {0003-889X},
     CODEN = {ACVMAL},
   MRCLASS = {12F10 (12E10 12F12)},
  MRNUMBER = {MR1174401 (93h:12004)},
MRREVIEWER = {R. W. K. Odoni},
}
@article {arxiv:0803.2836,
    AUTHOR = {Stoll, Michael},
     TITLE = {Rational 6-cycles under iteration of quadratic polynomials},
   JOURNAL = {LMS J. Comput. Math.},
  FJOURNAL = {LMS Journal of Computation and Mathematics},
    VOLUME = {11},
      YEAR = {2008},
     PAGES = {367--380},
      ISSN = {1461-1570},
   MRCLASS = {11G30 (11D41 11G40 14Gxx)},
  MRNUMBER = {MR2465796},
}
@comment{arxiv1308.4992}
@article {MR3273498,
    AUTHOR = {Stout, Brian Justin},
     TITLE = {A dynamical {S}hafarevich theorem for twists of rational
              morphisms},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {166},
      YEAR = {2014},
    NUMBER = {1},
     PAGES = {69--80},
      ISSN = {0065-1036},
   MRCLASS = {37P45 (14G25 37P15)},
  MRNUMBER = {3273498},
}
@comment{arxiv1309.5417}
@article {MR3253313,
    AUTHOR = {Stout, Brian and Towsley, Adam},
     TITLE = {Endomorphisms of bounded height and resultant},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {145},
      YEAR = {2014},
     PAGES = {426--432},
      ISSN = {0022-314X},
   MRCLASS = {37P45 (14D20)},
  MRNUMBER = {3253313},
       DOI = {10.1016/j.jnt.2014.06.006},
       URL = {http://dx.doi.org/10.1016/j.jnt.2014.06.006},
}
@article {MR2377368,
    AUTHOR = {Streng, Marco},
     TITLE = {Divisibility sequences for elliptic curves with complex
              multiplication},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {2},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {183--208},
      ISSN = {1937-0652},
   MRCLASS = {11G05 (11G15 14H52 14K22)},
  MRNUMBER = {2377368 (2009e:11110)},
MRREVIEWER = {Ambrus P{\'a}l},
       DOI = {10.2140/ant.2008.2.183},
       URL = {http://dx.doi.org/10.2140/ant.2008.2.183},
}
@article {MR3720796,
    AUTHOR = {Sugiyama, Toshi},
     TITLE = {The moduli space of polynomial maps and their fixed-point
              multipliers},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {322},
      YEAR = {2017},
     PAGES = {132--185},
      ISSN = {0001-8708},
   MRCLASS = {37F10 (14C17 14D20 37C25)},
  MRNUMBER = {3720796},
MRREVIEWER = {Fabrizio Bianchi},
       DOI = {10.1016/j.aim.2017.10.013},
       URL = {https://doi.org/10.1016/j.aim.2017.10.013},
}
@article {sullivan:nowanderingdomains,
    AUTHOR = {Sullivan, Dennis},
     TITLE = {Quasiconformal homeomorphisms and dynamics. {I}. {S}olution of
              the {F}atou-{J}ulia problem on wandering domains},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {122},
      YEAR = {1985},
    NUMBER = {3},
     PAGES = {401--418},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {58F11 (20H05 30C60 30D05 57R99 58F08)},
  MRNUMBER = {MR819553 (87i:58103)},
MRREVIEWER = {L. Keen},
}
@comment{UPDATE}
@misc {arxiv2102.12966,
    AUTHOR = {Suzuki, Fumiaki},
    TITLE = {Higher-dimensional {C}alabi-{Y}au varieties with dense sets of rational points},
     YEAR = {2021},
     NOTE = {\url{arXiv:2102.12966}},
}
@article {MR2099889,
    AUTHOR = {Svensson, P.-A.},
     TITLE = {Perturbed dynamical systems in {$p$}-adic fields},
   JOURNAL = {Tr. Mat. Inst. Steklova},
  FJOURNAL = {Trudy Matematicheskogo Instituta Imeni V. A. Steklova.
              Rossi\u\i skaya Akademiya Nauk},
    VOLUME = {245},
      YEAR = {2004},
    NUMBER = {Izbr. Vopr. $p$-adich. Mat. Fiz. i Anal.},
     PAGES = {264--272},
      ISSN = {0371-9685},
   MRCLASS = {11S85 (37F10)},
  MRNUMBER = {MR2099889 (2005h:11271)},
MRREVIEWER = {Liang-Chung Hsia},
}
@comment{UPDATE}
@misc {arxiv1407.7012,
    AUTHOR = {Swaminathan, Ashvin},
    TITLE = {On Arboreal {G}alois Representations of Rational Functions},
     YEAR = {2014},
     NOTE = {\url{arXiv:1407.7012}},
}
@comment{UPDATE}
@misc {arxiv2102.09684,
    AUTHOR = {Sing-Sweeney, Mark A.},
    TITLE = {A Dynamical Analogue of {S}en's Theorem},
     YEAR = {2021},
     NOTE = {\url{arXiv:2102.09684}},
}
@comment{UPDATE}
@misc {arxiv2208.00359,
    AUTHOR = {Sing-Sweeney, Mark A.},
    TITLE = {A Dynamical Analogue of the Criterion of {N}{\'e}ron--{O}gg--{S}hafarevich},
     YEAR = {2022},
     NOTE = {\url{arXiv:2208.00359}},
}
@article {MR1505274,
    AUTHOR = {Sylvester, J. J.},
     TITLE = {On a Point in the Theory of Vulgar Fractions},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {3},
      YEAR = {1880},
    NUMBER = {4},
     PAGES = {332--335},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {Contributed Item},
  MRNUMBER = {MR1505274},
}

@article {MR1065151,
    AUTHOR = {Szpiro, L.},
     TITLE = {Discriminant et conducteur des courbes elliptiques},
      NOTE = {S{\'e}minaire sur les Pinceaux de Courbes Elliptiques (Paris,
              1988)},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {183},
      YEAR = {1990},
     PAGES = {7--18},
      ISSN = {0303-1179},
   MRCLASS = {11G05 (11D41 14G25)},
  MRNUMBER = {1065151 (91g:11059)},
MRREVIEWER = {Philippe Satg{\'e}},
}
@comment{UPDATE}
@misc {SzpiroFieldsTalk2017,
    AUTHOR = {Szpiro, Lucien and Tucker, Thomas and West,Lloyd},
     TITLE = {Proof of the {S}hafarevich conjecture for self-maps of $\mathbb{P}^1$},
      YEAR = {February 13--17, 2017},
      NOTE = {Lecture at a Workshop on Heights and Applications to Unlikely Intersections,
      The Fields Institute, Toronto, \url{www.fields.utoronto.ca/talks/Proof-Shafarevich-conjecture-self-maps-mathbbP1}},
}
@comment{arxiv1010.5030}
@article {MR3264499,
    AUTHOR = {Szpiro, Lucien and Tepper, Michael and Williams, Phillip},
     TITLE = {Resultant and conductor of geometrically semi-stable self maps
              of the projective line over a number field or function field},
   JOURNAL = {Publ. Mat.},
  FJOURNAL = {Publicacions Matem\`atiques},
    VOLUME = {58},
      YEAR = {2014},
    NUMBER = {2},
     PAGES = {295--329},
      ISSN = {0214-1493},
   MRCLASS = {37P05 (11G05 14G25 37P45)},
  MRNUMBER = {3264499},
       URL = {http://projecteuclid.org/euclid.pm/1405949320},
}
@comment{arxiv1212.3391}
@article {MR3119234,
    AUTHOR = {Szpiro, Lucien and Tepper, Michael and Williams, Phillip},
     TITLE = {Semi-stable reduction implies minimality of the resultant},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {397},
      YEAR = {2014},
     PAGES = {489--498},
      ISSN = {0021-8693},
   MRCLASS = {14E05 (13P15)},
  MRNUMBER = {3119234},
MRREVIEWER = {Shu Kawaguchi},
       URL = {https://doi.org/10.1016/j.jalgebra.2013.09.008},
}
@incollection {arxiv0510404,
    AUTHOR = {Szpiro, L. and Tucker, T. J.},
     TITLE = {Equidistribution and generalized {M}ahler measures},
 BOOKTITLE = {Number theory, analysis and geometry},
     PAGES = {609--638},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2012},
   MRCLASS = {37P30 (11J68 37P35)},
  MRNUMBER = {2867934},
MRREVIEWER = {Charles Favre},
       DOI = {10.1007/978-1-4614-1260-1_26},
       URL = {http://dx.doi.org/10.1007/978-1-4614-1260-1_26},
}
@incollection {arxiv0603438,
    AUTHOR = {Szpiro, Lucien and Tucker, Thomas J.},
     TITLE = {On half log discriminant},
 BOOKTITLE = {Diophantine geometry},
    SERIES = {CRM Series},
    VOLUME = {4},
     PAGES = {323--334},
 PUBLISHER = {Ed. Norm., Pisa},
      YEAR = {2007},
   MRCLASS = {11G35},
  MRNUMBER = {MR2349664 (2008k:11071)},
MRREVIEWER = {Charles Favre},
}

@article  {arxiv0603436,
    AUTHOR = {Szpiro, Lucien and Tucker, Thomas J.},
     TITLE = {A {S}hafarevich-{F}altings theorem for rational functions},
   JOURNAL = {Pure Appl. Math. Q.},
  FJOURNAL = {Pure and Applied Mathematics Quarterly},
    VOLUME = {4},
      YEAR = {2008},
    NUMBER = {3, part 2},
     PAGES = {715--728},
      ISSN = {1558-8599},
   MRCLASS = {14G25},
  MRNUMBER = {MR2435841 (2009g:14027)},
MRREVIEWER = {Marco A. Garuti},
}

@article {MR1427622,
    AUTHOR = {Szpiro, L. and Ullmo, E. and Zhang, S.},
     TITLE = {\'{E}quir\'epartition des petits points},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {127},
      YEAR = {1997},
    NUMBER = {2},
     PAGES = {337--347},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14G40 (11G35 14G05)},
  MRNUMBER = {MR1427622 (98i:14027)},
MRREVIEWER = {Antoine Chambert-Loir},
}
@comment{UPDATE}
@misc {arxiv1705.05489,
    AUTHOR = {Szpiro, L. and West, L.},
    TITLE = {A dynamical {S}hafarevich theorem for rational maps over number fields and function fields},
     YEAR = {2017},
     NOTE = {\url{arXiv:1705.05489}},
}


@comment{--TTT-- }

@comment{Tai proves A_g is general type for all g \ge 9}
@article {MR669424,
    AUTHOR = {Tai, Yung-Sheng},
     TITLE = {On the {K}odaira dimension of the moduli space of abelian
              varieties},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {68},
      YEAR = {1982},
    NUMBER = {3},
     PAGES = {425--439},
      ISSN = {0020-9910},
   MRCLASS = {10D20 (14D20 14K05 32N05)},
  MRNUMBER = {669424},
MRREVIEWER = {K.-B. Gundlach},
       DOI = {10.1007/BF01389411},
       URL = {https://doi.org/10.1007/BF01389411},
}
@article {MR3780009,
    AUTHOR = {Talamini, Vittorino},
     TITLE = {Canonical bases of invariant polynomials for the irreducible
              reflection groups of types {$E_6$}, {$E_7$}, and {$E_8$}},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {503},
      YEAR = {2018},
     PAGES = {590--603},
      ISSN = {0021-8693},
   MRCLASS = {20F55 (13A50)},
  MRNUMBER = {3780009},
MRREVIEWER = {Zinovy Reichstein},
       DOI = {10.1016/j.jalgebra.2018.01.017},
       URL = {https://doi.org/10.1016/j.jalgebra.2018.01.017},
}
@misc {TateHaverford,
    AUTHOR = {Tate, John T.},
    TITLE = {Rational points on cubic curves},
     YEAR = {1961},
     NOTE = {Unpublished notes of lectures delivered at Haverford College},
}
@article {MR0419359,
    AUTHOR = {Tate, John T.},
     TITLE = {The arithmetic of elliptic curves},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {23},
      YEAR = {1974},
     PAGES = {179--206},
      ISSN = {0020-9910},
   MRCLASS = {10D05 (14G25 14K15)},
  MRNUMBER = {0419359},
MRREVIEWER = {A. P. Ogg},
}
@article {MR692114,
    AUTHOR = {Tate, J.},
     TITLE = {Variation of the canonical height of a point depending on a
              parameter},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {105},
      YEAR = {1983},
    NUMBER = {1},
     PAGES = {287--294},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {14K15 (14G25 14K10)},
  MRNUMBER = {692114 (84k:14034)},
MRREVIEWER = {M. Bashmakov},
       DOI = {10.2307/2374389},
       URL = {http://dx.doi.org/10.2307/2374389},
}
@article {MR0393039,
    AUTHOR = {Tate, J.},
     TITLE = {Algorithm for determining the type of a singular fiber in an
              elliptic pencil},
 BOOKTITLE = {Modular functions of one variable, {IV} ({P}roc. {I}nternat.
              {S}ummer {S}chool, {U}niv. {A}ntwerp, {A}ntwerp, 1972)},
     PAGES = {33--52. Lecture Notes in Math., Vol. 476},
 PUBLISHER = {Springer, Berlin},
      YEAR = {1975},
   MRCLASS = {14G25 (14K15)},
  MRNUMBER = {0393039},
MRREVIEWER = {J. S. Milne},
}
@article {thiran:padicdynamics,
   AUTHOR = {Thiran, E. and Verstegen, D. and Weyers, J.},
    TITLE = {$p$-adic dynamics},
  JOURNAL = {J. Statist. Phys.},
 FJOURNAL = {Journal of Statistical Physics},
   VOLUME = {54},
     YEAR = {1989},
   NUMBER = {3-4},
    PAGES = {893--913},
}

@comment{Has a nice summary/overview of GIT}
@incollection {MR2408226,
    AUTHOR = {Thomas, R. P.},
     TITLE = {Notes on {GIT} and symplectic reduction for bundles and
              varieties},
 BOOKTITLE = {Surveys in differential geometry. {V}ol. {X}},
    SERIES = {Surv. Differ. Geom.},
    VOLUME = {10},
     PAGES = {221--273},
 PUBLISHER = {Int. Press, Somerville, MA},
      YEAR = {2006},
   MRCLASS = {14L24 (32Q20 53D20)},
  MRNUMBER = {2408226},
MRREVIEWER = {Nicholas J. Proudfoot},
       DOI = {10.4310/SDG.2005.v10.n1.a7},
      NOTE = {arXiv:math/0512411},
}

@phdthesis{thuillier:thesis, 
   AUTHOR = {Thuillier, Amaury},
    TITLE = {Th{\'e}orie du potentiel sur les courbes en
        g{\'e}om{\'e}trie analytique non
        archim{\'e}dienne. {A}pplications \`a la th{\'e}orie
        d'{A}rakelov},
   SCHOOL = {Universit\'e Rennes},
     YEAR = {2005}
}
@article {MR1028906,
    AUTHOR = {Tischler, David},
     TITLE = {Critical points and values of complex polynomials},
   JOURNAL = {J. Complexity},
  FJOURNAL = {Journal of Complexity},
    VOLUME = {5},
      YEAR = {1989},
    NUMBER = {4},
     PAGES = {438--456},
      ISSN = {0885-064X},
   MRCLASS = {30C10},
  MRNUMBER = {1028906 (91a:30004)},
MRREVIEWER = {J. Matkowski},
}
@comment{UPDATE}
@misc {arxiv1209.2399,
    AUTHOR = {Towsley, Adam},
    TITLE = {A {H}asse Principle for Periodic Points},
     YEAR = {2012},
     NOTE = {\url{arXiv:1209.2399}},
}
@article {MR3689669,
    AUTHOR = {Troncoso, Sebastian},
     TITLE = {Bounds for preperiodic points for maps with good reduction},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {181},
      YEAR = {2017},
     PAGES = {51--72},
      ISSN = {0022-314X},
   MRCLASS = {37P05 (11D45)},
  MRNUMBER = {3689669},
       URL = {https://doi.org/10.1016/j.jnt.2017.05.026},
}
@article {MR3295719,
    AUTHOR = {Trucco, Eugenio},
     TITLE = {Wandering {F}atou components and algebraic {J}ulia sets},
   JOURNAL = {Bull. Soc. Math. France},
  FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France},
    VOLUME = {142},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {411--464},
      ISSN = {0037-9484},
   MRCLASS = {37P40 (37F50 37P05 37P50)},
  MRNUMBER = {3295719},
MRREVIEWER = {Y\^usuke Okuyama},
}
@article {MR3375933,
    AUTHOR = {Trucco, Eugenio},
     TITLE = {On {F}ibonacci polynomials and wandering domains},
   JOURNAL = {Bull. Lond. Math. Soc.},
  FJOURNAL = {Bulletin of the London Mathematical Society},
    VOLUME = {47},
      YEAR = {2015},
    NUMBER = {4},
     PAGES = {663--674},
      ISSN = {0024-6093},
   MRCLASS = {37P05 (11S82 37F20 37P40)},
  MRNUMBER = {3375933},
MRREVIEWER = {Lingmin Liao},
       DOI = {10.1112/blms/bdv046},
       URL = {https://doi.org/10.1112/blms/bdv046},
}
@article {MR2497321,
    AUTHOR = {Truong, Tuyen Trung},
     TITLE = {Degree complexity of a family of birational maps. {II}.
              {E}xceptional cases},
   JOURNAL = {Math. Phys. Anal. Geom.},
  FJOURNAL = {Mathematical Physics, Analysis and Geometry. An International
              Journal Devoted to the Theory and Applications of Analysis and
              Geometry to Physics},
    VOLUME = {12},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {157--180},
      ISSN = {1385-0172},
     CODEN = {MPAGFO},
   MRCLASS = {32H50 (37F10 54E05)},
  MRNUMBER = {2497321 (2010c:32031)},
MRREVIEWER = {Julie D{\'e}serti},
       DOI = {10.1007/s11040-009-9057-z},
       URL = {http://dx.doi.org/10.1007/s11040-009-9057-z},
}
@comment{arxiv1605.05049}
@article {MR4048444,
    AUTHOR = {Truong, Tuyen Trung},
     TITLE = {Relative dynamical degrees of correspondences over a field of
              arbitrary characteristic},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {758},
      YEAR = {2020},
     PAGES = {139--182},
      ISSN = {0075-4102},
   MRCLASS = {37P05 (14E05 37F05 37F80)},
  MRNUMBER = {4048444},
       DOI = {10.1515/crelle-2017-0052},
       URL = {https://doi.org/10.1515/crelle-2017-0052},
}
@article {MR3744855,
    AUTHOR = {Tsimerman, Jacob},
     TITLE = {The {A}ndr\'{e}-{O}ort conjecture for {$\mathcal{A}_g$}},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {187},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {379--390},
      ISSN = {0003-486X},
   MRCLASS = {11G15 (11G18 14G35)},
  MRNUMBER = {3744855},
MRREVIEWER = {Patrick Morton},
       DOI = {10.4007/annals.2018.187.2.2},
       URL = {https://doi.org/10.4007/annals.2018.187.2.2},
}
@comment{--UUU-- }

@article {MR2380321,
    AUTHOR = {Uchida, Yukihiro},
     TITLE = {The difference between the ordinary height and the canonical
              height on elliptic curves},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {128},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {263--279},
      ISSN = {0022-314X},
   MRCLASS = {11G50 (11G05 11G07)},
  MRNUMBER = {2380321},
MRREVIEWER = {Clayton Petsche},
       DOI = {10.1016/j.jnt.2007.10.002},
       URL = {https://doi.org/10.1016/j.jnt.2007.10.002},
}
@article {MR1251576,
    AUTHOR = {Ueda, Tetsuo},
     TITLE = {Complex dynamical systems on projective spaces},
      NOTE = {Topics around chaotic dynamical systems (Japanese) (Kyoto,
              1992)},
   JOURNAL = {S\=urikaisekikenky\=usho K\=oky\=uroku},
  FJOURNAL = {S\=urikaisekikenky\=usho K\=oky\=uroku},
    NUMBER = {814},
      YEAR = {1992},
     PAGES = {169--186},
   MRCLASS = {32H50 (58F23)},
  MRNUMBER = {1251576},
}
@incollection {MR1479941,
    AUTHOR = {Ueda, Tetsuo},
     TITLE = {Complex dynamics on projective spaces---index formula for
              fixed points},
 BOOKTITLE = {Dynamical systems and chaos, {V}ol. 1 ({H}achioji, 1994)},
     PAGES = {252--259},
 PUBLISHER = {World Sci. Publ., River Edge, NJ},
      YEAR = {1995},
   MRCLASS = {32H50},
  MRNUMBER = {1479941},
MRREVIEWER = {Marco Abate},
}
@incollection {MR1747345,
    AUTHOR = {Ueda, Tetsuo},
     TITLE = {Critically finite maps on projective spaces},
      NOTE = {Research on complex dynamical systems: current state and
              prospects (Japanese) (Kyoto, 1998)},
   JOURNAL = {S\={u}rikaisekikenky\={u}sho K\B{o}ky\={u}roku},
  FJOURNAL = {S\={u}rikaisekikenky\={u}sho K\B{o}ky\={u}roku},
    NUMBER = {1087},
      YEAR = {1999},
     PAGES = {132--138},
   MRCLASS = {32H50 (37F10)},
  MRNUMBER = {1747345},
}
@misc {UedaIML2008,
    AUTHOR = {Ueda, Tetsuo},
     TITLE = {Critically finite holomorphic maps on projective spaces},
      NOTE = {Institue Mittag-Leffler, Report No. 38, 2007/2008, spring},
}
@article {MR3475294,
    AUTHOR = {Ueno, Kohei},
     TITLE = {B\"ottcher coordinates at superattracting fixed points of
              holomorphic skew products},
   JOURNAL = {Conform. Geom. Dyn.},
  FJOURNAL = {Conformal Geometry and Dynamics. An Electronic Journal of the
              American Mathematical Society},
    VOLUME = {20},
      YEAR = {2016},
     PAGES = {43--57},
      ISSN = {1088-4173},
   MRCLASS = {32H50},
  MRNUMBER = {3475294},
MRREVIEWER = {Scott R. Kaschner},
       DOI = {10.1090/ecgd/290},
       URL = {https://doi.org/10.1090/ecgd/290},
}
@incollection {arxiv1107.4565,
    AUTHOR = {Ugolini, S.},
     TITLE = {Graphs associated with the map {$x\mapsto x+x^{-1}$} in
              finite fields of characteristic two},
 BOOKTITLE = {Theory and applications of finite fields},
    SERIES = {Contemp. Math.},
    VOLUME = {579},
     PAGES = {187--204},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2012},
   MRCLASS = {37P55 (05C20 05C25 11T30 37P35)},
  MRNUMBER = {2975769},
MRREVIEWER = {Jeffrey O. Shallit},
       DOI = {10.1090/conm/579/11530},
       URL = {http://dx.doi.org/10.1090/conm/579/11530},
}
@article {arxiv1110.0968,
    AUTHOR = {Ugolini, S.},
     TITLE = {Graphs associated with the map {$X\mapsto X+X^{-1}$} in
              finite fields of characteristic three and five},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {133},
      YEAR = {2013},
    NUMBER = {4},
     PAGES = {1207--1228},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11G20},
  MRNUMBER = {3003995},
       DOI = {10.1016/j.jnt.2012.09.007},
       URL = {http://dx.doi.org/10.1016/j.jnt.2012.09.007},
}
@comment{UPDATE}
@misc {arxiv1207.6959,
    AUTHOR = {Ugolini, Simone},
    TITLE = {Iterations of the map $X \mapsto \frac{1}{2} (X + X^{-1}) $ 
         over finite fields of odd characteristic and sequences of 
         irreducible polynomials},
     YEAR = {2012},
     NOTE = {\url{arXiv:1207.6959}},
}
@comment{arxiv1304.3283}
@article {MR3208403,
    AUTHOR = {Ugolini, S.},
     TITLE = {On the iterations of certain maps {$X\mapsto
              K\cdot(X+X^{-1})$} over finite fields of odd characteristic},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {142},
      YEAR = {2014},
     PAGES = {274--297},
      ISSN = {0022-314X},
   MRCLASS = {37P05 (11T06)},
  MRNUMBER = {3208403},
       URL = {https://doi.org/10.1016/j.jnt.2014.02.024},
}
@comment{UPDATE}
@misc {arxiv1308.6723,
    AUTHOR = {Ugolini, Simone},
    TITLE = {Sequences of irreducible polynomials over odd prime
                  fields via elliptic curve endomorphisms},
     YEAR = {2013},
     NOTE = {\url{arXiv:1308.6723}},
}
@comment{arxiv1509.05365}
@article {MR3866630,
    AUTHOR = {Ugolini, S.},
     TITLE = {Functional graphs of rational maps induced by endomorphisms of
              ordinary elliptic curves over finite fields},
   JOURNAL = {Period. Math. Hungar.},
  FJOURNAL = {Periodica Mathematica Hungarica. Journal of the J\'{a}nos Bolyai
              Mathematical Society},
    VOLUME = {77},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {237--260},
      ISSN = {0031-5303},
   MRCLASS = {37P55 (11G20 37P05)},
  MRNUMBER = {3866630},
       DOI = {10.1007/s10998-018-0242-3},
       URL = {https://doi.org/10.1007/s10998-018-0242-3},
}
@article {MR4059865,
    AUTHOR = {Ugolini, Simone},
     TITLE = {Some notes on the multiplicative order of {$\alpha + \alpha
              ^{-1}$} in finite fields of characteristic two},
   JOURNAL = {Period. Math. Hungar.},
  FJOURNAL = {Periodica Mathematica Hungarica. Journal of the J\'{a}nos Bolyai
              Mathematical Society},
    VOLUME = {80},
      YEAR = {2020},
    NUMBER = {1},
     PAGES = {81--94},
      ISSN = {0031-5303},
   MRCLASS = {11T30 (11G20 37P55)},
  MRNUMBER = {4059865},
       DOI = {10.1007/s10998-019-00296-z},
       URL = {https://doi.org/10.1007/s10998-019-00296-z},
}
@article {MR1609514,
    AUTHOR = {Ullmo, Emmanuel},
     TITLE = {Positivit\'e et discr\'etion des points alg\'ebriques des
              courbes},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {147},
      YEAR = {1998},
    NUMBER = {1},
     PAGES = {167--179},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {14G40 (11G30 14H25 14H40)},
  MRNUMBER = {MR1609514 (99e:14031)},
MRREVIEWER = {Yuichiro Takeda},
}
@article {MR3245008,
    AUTHOR = {Ullmo, Emmanuel and Yafaev, Andrei},
     TITLE = {Galois orbits and equidistribution of special subvarieties:
              towards the {A}ndr\'{e}-{O}ort conjecture},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {180},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {823--865},
      ISSN = {0003-486X},
   MRCLASS = {11G18 (14G35)},
  MRNUMBER = {3245008},
MRREVIEWER = {Christopher Daw},
       DOI = {10.4007/annals.2014.180.3.1},
       URL = {https://doi.org/10.4007/annals.2014.180.3.1},
}
@comment{arxiv1606.04822}
@article {MR3818624,
    AUTHOR = {Urech, Christian},
     TITLE = {Remarks on the degree growth of birational transformations},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {25},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {291--308},
      ISSN = {1073-2780},
   MRCLASS = {37P05 (14E07 32H50 37C35)},
  MRNUMBER = {3818624},
       DOI = {10.4310/mrl.2018.v25.n1.a13},
       URL = {https://doi.org/10.4310/mrl.2018.v25.n1.a13},
}
@COMMENT{This does not seem to be in MR}
@incollection {ushiki1992,
   AUTHOR = {Ushiki, Shigehiro},
    TITLE = {B\"ottcher’s theorem and super-stable manifolds for multidimensional complex dynamical systems},
   EDITOR = {S. Ushiki},
BOOKTITLE = {Proceedings of the RIMS Conference Structure and Bifurcations of Dynamical Systems, 18--21 February 1992, Kyoto, Japan},
     NOTE = {Advanced Series in Dynamical Systems},
   VOLUME = {11},
PUBLISHER = {World Scientific Publishing Co.},
     YEAR = {1992},
    PAGES = {168--184},
}


@comment{--VVV-- }

@article {MR738261,
    AUTHOR = {Vainsencher, Israel},
     TITLE = {Complete collineations and blowing up determinantal ideals},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {267},
      YEAR = {1984},
    NUMBER = {3},
     PAGES = {417--432},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {14M12 (14N10)},
  MRNUMBER = {738261 (85f:14053)},
MRREVIEWER = {Tadeusz J{\'o}zefiak},
       DOI = {10.1007/BF01456098},
       URL = {http://dx.doi.org/10.1007/BF01456098},
}
@book{vanderwaerden:algebra, 
   AUTHOR = {van der Waerden, B.L.},
    TITLE = {Algebra},
  EDITION = {7th},
PUBLISHER = {Frederick Ungar Publ. Co.},
  ADDRESS = {New York},
     YEAR = {1970}
}
@article {MR2033734,
    AUTHOR = {Vasiga, Troy and Shallit, Jeffrey},
     TITLE = {On the iteration of certain quadratic maps over {$\operatorname{GF}(p)$}},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {277},
      YEAR = {2004},
    NUMBER = {1-3},
     PAGES = {219--240},
      ISSN = {0012-365X},
     CODEN = {DSMHA4},
   MRCLASS = {05C20 (11T99)},
  MRNUMBER = {MR2033734 (2004k:05104)},
MRREVIEWER = {Kevin Lawrence McAvaney},
}
@comment{From MR: For a finite set $S$ and a function $f\colon S\rightarrow S$, the directed graph $G_f$ has vertex set $S$ and
directed edges $(x,f(x))$ for all $x$ in $S$. Thus, $G_f$ depicts the
iterations of $f$: each $x$ induces a path (tail) attached to a
cycle. Motivated by various factoring and prime testing algorithms in
number theory the authors investigate the structure of $G_f$ for
$f(x)=x^2\pmod{p}$ and $f(x)=x^2-2\pmod{p}$ for prime $p$. In
particular they give the complete structure for both functions when
$p$ is a Fermat prime or a Mersenne prime. For general $p$ average
tail and cycle lengths in $G_f$ are determined and some asymptotic
results are given.
For a generalization to f(x)=x^e in finite fields, see:
MR2072394 (2005e:11118) Chou, Wun-Seng(RC-AST); Shparlinski, Igor
E.(5-MCQR-CP) On the cycle structure of repeated exponentiation modulo
a prime. (English summary) J. Number Theory 107 (2004), no. 2,
345--356. }
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@incollection {MR1098340,
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@comment{arxiv1307.3205}
@article {MR3159393,
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@comment{arxiv1504.07099}
@article {MR3470673,
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@comment{arxiv1711.06345}
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@incollection {MR2757629,
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}
@comment{UPDATE}
@misc {arxiv1806.10737,
    AUTHOR = {Vojta, Paul},
    TITLE = {{R}oth's Theorem for arithmetic function fields},
     YEAR = {2018},
     NOTE = {\url{arXiv:1806.10737}},
}
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    VOLUME = {74},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {81--95},
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     CODEN = {AARIA9},
   MRCLASS = {11J25 (11R06)},
  MRNUMBER = {MR1367580 (96j:11098)},
MRREVIEWER = {D. Boyd},
}
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@comment{--WWW-- }

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@comment{UPDATE}
@misc {arxiv2009.14382,
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     YEAR = {2020},
     NOTE = {\url{arXiv:2009.14382}},
}
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@comment{arxiv1403.3975}
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@comment{UPDATE}
@misc {arxiv2201.12750,
    AUTHOR = {Wang, Long},
    TITLE = {Periodic points and arithmetic degrees of certain birational self-maps},
     YEAR = {2022},
     NOTE = {\url{arXiv:2201.12750}},
}
@comment{UPDATE}
@misc {arxiv1504.00985,
    AUTHOR = {Wang, Zhiming and Zhang, Robin},
    TITLE = {On quadratic periodic points of quadratic polynomials},
     YEAR = {2015},
     NOTE = {\url{arXiv:1504.00985}},
}
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MRREVIEWER = {H. S. Zuckerman},
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     YEAR = {1998},
   NUMBER = {2},
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   MRCLASS = {11R18 (11-01 11-02 11R23)},
  MRNUMBER = {MR1421575 (97h:11130)},
MRREVIEWER = {T. Mets{\"a}nkyl{\"a}},
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@article {MR925498,
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    VOLUME = {50},
      YEAR = {1988},
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@article {MR0082726,
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    VOLUME = {78},
      YEAR = {1956},
     PAGES = {509--524},
      ISSN = {0002-9327},
   MRCLASS = {14.0X},
  MRNUMBER = {0082726},
MRREVIEWER = {P. Samuel},
       DOI = {10.2307/2372670},
       URL = {https://doi.org/10.2307/2372670},
}
@comment{UPDATE}
@misc {arxiv2104.06211,
    AUTHOR = {Weinreich, Max},
    TITLE = {The Algebraic Dynamics of the Pentagram Map},
     YEAR = {2021},
     NOTE = {\url{arXiv:2104.06211}},
}
@article {MR2943169,
    AUTHOR = {Weisz, Ferenc},
     TITLE = {Summability of multi-dimensional trigonometric {F}ourier
              series},
   JOURNAL = {Surv. Approx. Theory},
  FJOURNAL = {Surveys in Approximation Theory},
    VOLUME = {7},
      YEAR = {2012},
     PAGES = {1--179},
   MRCLASS = {42B08 (42A38 42B30)},
  MRNUMBER = {2943169},
MRREVIEWER = {Juan Luis Varona},
      NOTE = {https://arxiv.org/pdf/1206.1789.pdf},
}
@article {MR3667036,
    AUTHOR = {Wells, Elliot},
     TITLE = {Computing canonical heights on the projective line with no
              factorization},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {86},
      YEAR = {2017},
    NUMBER = {308},
     PAGES = {3019--3029},
      ISSN = {0025-5718},
   MRCLASS = {37P30 (11G50 11Y16)},
  MRNUMBER = {3667036},
MRREVIEWER = {Lukas Pottmeyer},
       URL = {https://doi.org/10.1090/mcom/3200},
}
@article {MR1458753,
    AUTHOR = {Werner, Annette},
     TITLE = {Local heights on abelian varieties with split multiplicative
              reduction},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {107},
      YEAR = {1997},
    NUMBER = {3},
     PAGES = {289--317},
      ISSN = {0010-437X},
   MRCLASS = {14K05 (14K25)},
  MRNUMBER = {1458753},
MRREVIEWER = {Dan Abramovich},
       DOI = {10.1023/A:1000139010486},
       URL = {https://doi.org/10.1023/A:1000139010486},
}

@article {MR1662481,
    AUTHOR = {Werner, Annette},
     TITLE = {Local heights on abelian varieties and rigid analytic
              uniformization},
   JOURNAL = {Doc. Math.},
  FJOURNAL = {Documenta Mathematica},
    VOLUME = {3},
      YEAR = {1998},
     PAGES = {301--319},
      ISSN = {1431-0635},
   MRCLASS = {11G10 (11G25 14G20 14K15)},
  MRNUMBER = {1662481},
MRREVIEWER = {Carlo Gasbarri},
}		

@article {MR1418354,
    AUTHOR = {Werner, Annette},
     TITLE = {Local heights on {M}umford curves},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {306},
      YEAR = {1996},
    NUMBER = {4},
     PAGES = {819--831},
      ISSN = {0025-5831},
   MRCLASS = {14G20 (14H25)},
  MRNUMBER = {1418354},
MRREVIEWER = {Genady Lazarevich Margolin},
       DOI = {10.1007/BF01445278},
       URL = {https://doi.org/10.1007/BF01445278},
}
		
@comment{UPDATE}
@misc {arxiv1408.3247,
    AUTHOR = {West, Lloyd},
    TITLE = {The Moduli Space of Cubic Rational Maps},
     YEAR = {2014},
     NOTE = {\url{arXiv:1408.3247}},
}

@book {MR3427313,
    AUTHOR = {West, Lloyd William},
     TITLE = {The {M}oduli {S}pace of {R}ational {M}aps},
      NOTE = {Thesis (Ph.D.)--City University of New York},
 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {2015},
     PAGES = {88},
      ISBN = {978-1339-02142-3},
   MRCLASS = {Thesis},
  MRNUMBER = {3427313},
}
@article {MR3323197,
    AUTHOR = {Wibmer, Michael},
     TITLE = {Skolem-{M}ahler-{L}ech type theorems and {P}icard-{V}essiot
              theory},
   JOURNAL = {J. Eur. Math. Soc. (JEMS)},
  FJOURNAL = {Journal of the European Mathematical Society (JEMS)},
    VOLUME = {17},
      YEAR = {2015},
    NUMBER = {3},
     PAGES = {523--533},
      ISSN = {1435-9855},
   MRCLASS = {39A06 (11B25 11B37)},
  MRNUMBER = {3323197},
       DOI = {10.4171/JEMS/509},
       URL = {https://doi.org/10.4171/JEMS/509},
}
@comment{UPDATE}
@misc {arxiv2101.11593,
    AUTHOR = {Wilms, Robert},
    TITLE = {An explicit and uniform {M}anin--{M}umford-type result for function fields},
     YEAR = {2021},
     NOTE = {\url{arXiv:2101.11593}},
}
@book {MR1612686,
    AUTHOR = {Wirsching, G{\"u}nther J.},
     TITLE = {The dynamical system generated by the {$3n+1$} function},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {1681},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1998},
     PAGES = {viii+158},
      ISBN = {3-540-63970-5},
   MRCLASS = {11B83 (11B37 11K41 39B12 58F08 60C05 60J10)},
  MRNUMBER = {MR1612686 (99g:11027)},
MRREVIEWER = {J. C. Lagarias},
}
@article {MR937529,
    AUTHOR = {Withers, Wm. Douglas},
     TITLE = {Folding polynomials and their dynamics},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {American Mathematical Monthly},
    VOLUME = {95},
      YEAR = {1988},
    NUMBER = {5},
     PAGES = {399--413},
      ISSN = {0002-9890},
   MRCLASS = {58F25 (26C05 58F08)},
  MRNUMBER = {937529},
MRREVIEWER = {M. Mend\`es France},
       DOI = {10.2307/2322475},
       URL = {https://doi.org/10.2307/2322475},
}
@article {woodcocksmart:chaosprng,
   AUTHOR = {Woodcock, Christopher F. and Smart, Nigel P.},
    TITLE = {$p$-adic chaos and random number generation},
  JOURNAL = {Experiment. Math.},
 FJOURNAL = {Experimental Mathematics},
   VOLUME = {7},
     YEAR = {1998},
   NUMBER = {4},
    PAGES = {333--342},
}
@article {MR3072752,
    AUTHOR = {Worden, William},
     TITLE = {Iterations of quadratic polynomials over finite fields},
   JOURNAL = {Involve},
  FJOURNAL = {Involve. A Journal of Mathematics},
    VOLUME = {6},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {99--112},
      ISSN = {1944-4176},
   MRCLASS = {37P05 (11B37)},
  MRNUMBER = {3072752},
MRREVIEWER = {Thomas Ward},
       DOI = {10.2140/involve.2013.6.99},
       URL = {http://dx.doi.org/10.2140/involve.2013.6.99},
}
@comment{--XXX-- }

@comment{Original ArXiv version has slightly different title: arXiv:1106.1825}
@comment{Section 5 has reduction of dynamical degree modulo p}
@article {arxiv1106.1825,
    AUTHOR = {Xie, Junyi},
     TITLE = {Periodic points of birational transformations on projective
              surfaces},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {164},
      YEAR = {2015},
    NUMBER = {5},
     PAGES = {903--932},
      ISSN = {0012-7094},
   MRCLASS = {37P55 (14E05 37C25)},
  MRNUMBER = {3332894},
       DOI = {10.1215/00127094-2877402},
       URL = {http://dx.doi.org/10.1215/00127094-2877402},
}
@article {MR3263169,
    AUTHOR = {Xie, Junyi},
     TITLE = {Dynamical {M}ordell-{L}ang conjecture for birational
              polynomial morphisms on {$\mathbb{A}^2$}},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {360},
      YEAR = {2014},
    NUMBER = {1-2},
     PAGES = {457--480},
      ISSN = {0025-5831},
   MRCLASS = {37P55 (14E05 14R10 37P05)},
  MRNUMBER = {3263169},
MRREVIEWER = {Tatiana M. Bandman},
       DOI = {10.1007/s00208-014-1039-1},
       URL = {http://dx.doi.org/10.1007/s00208-014-1039-1},
}
@COMMENT{arxiv1503.00773}
@article {MR3758955,
    AUTHOR = {Xie, Junyi},
     TITLE = {The dynamical {M}ordell-{L}ang conjecture for polynomial
              endomorphisms of the affine plane},
   JOURNAL = {Ast\'{e}risque},
  FJOURNAL = {Ast\'{e}risque},
    NUMBER = {394},
      YEAR = {2017},
     PAGES = {vi+110},
      ISSN = {0303-1179},
      ISBN = {978-2-85629-869-5},
   MRCLASS = {37P05 (14R10)},
  MRNUMBER = {3758955},
MRREVIEWER = {Dragos Ghioca},
}

@article {MR3705271,
    AUTHOR = {Xie, Junyi},
     TITLE = {The existence of {Z}ariski dense orbits for polynomial
              endomorphisms of the affine plane},
   JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {153},
      YEAR = {2017},
    NUMBER = {8},
     PAGES = {1658--1672},
      ISSN = {0010-437X},
   MRCLASS = {37P55 (32H50)},
  MRNUMBER = {3705271},
       URL = {https://doi.org/10.1112/S0010437X17007187},
}
@COMMENT{arxiv1602.04253}
@article {MR3871508,
    AUTHOR = {Xie, Junyi},
     TITLE = {Algebraic dynamics of the lifts of {F}robenius},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {12},
      YEAR = {2018},
    NUMBER = {7},
     PAGES = {1715--1748},
      ISSN = {1937-0652},
   MRCLASS = {37P55 (37P20 37P35)},
  MRNUMBER = {3871508},
       DOI = {10.2140/ant.2018.12.1715},
       URL = {https://doi.org/10.2140/ant.2018.12.1715},
}
@inproceedings {MR3971897,
    AUTHOR = {Xie, Junyi},
     TITLE = {Algebraic actions of discrete groups},
 BOOKTITLE = {Proceedings of the {S}eventh {I}nternational {C}ongress of
              {C}hinese {M}athematicians. {V}ol. {II}},
    SERIES = {Adv. Lect. Math. (ALM)},
    VOLUME = {44},
     PAGES = {155--167},
 PUBLISHER = {Int. Press, Somerville, MA},
      YEAR = {2019},
   MRCLASS = {14E07 (37P20)},
  MRNUMBER = {3971897},
}

@comment{UPDATE}
@misc {arxiv2107.03559,
    AUTHOR = {Xie, Junyi},
    TITLE = {Remarks on algebraic dynamics in positive characteristic},
     YEAR = {2021},
     NOTE = {\url{arXiv:2107.03559}},
}
@comment{UPDATE}
@misc {arxiv2202.09032,
    AUTHOR = {Xie, Junyi},
    TITLE = {Algebraicity criteria, invariant subvarities and transcendence problems from arithmetic dynamics},
     YEAR = {2021},
     NOTE = {\url{arXiv:2202.09032}},
}

@comment{--YYY-- }

@article {MR3864775,
    AUTHOR = {Yang, Bo and Liao, Xiaofeng},
     TITLE = {Some characteristics of logistic map over the finite field},
   JOURNAL = {Sci. China Inf. Sci.},
  FJOURNAL = {Science China. Information Sciences},
    VOLUME = {62},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {039104, 3},
      ISSN = {1674-733X},
   MRCLASS = {37P25},
  MRNUMBER = {3864775},
       DOI = {10.1007/s11432-017-9438-8},
       URL = {https://doi.org/10.1007/s11432-017-9438-8},
}
@article {MR2846352,
    AUTHOR = {Yasufuku, Yu},
     TITLE = {Integral points and {V}ojta's conjecture on rational surfaces},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {364},
      YEAR = {2012},
    NUMBER = {2},
     PAGES = {767--784},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {11J97 (14G40 14J26)},
  MRNUMBER = {2846352},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.1090/S0002-9947-2011-05320-1},
       URL = {http://dx.doi.org/10.1090/S0002-9947-2011-05320-1},
}
@incollection {MR2868570,
    AUTHOR = {Yasufuku, Yu},
     TITLE = {Vojta's conjecture and dynamics},
 BOOKTITLE = {Algebraic number theory and related topics 2009},
    SERIES = {RIMS K\^oky\^uroku Bessatsu, B25},
     PAGES = {75--86},
 PUBLISHER = {Res. Inst. Math. Sci. (RIMS), Kyoto},
      YEAR = {2011},
   MRCLASS = {37P15 (11J97 37P55)},
  MRNUMBER = {2868570},
MRREVIEWER = {Joseph H. Silverman},
}
@article {MR3318263,
    AUTHOR = {Yasufuku, Yu},
     TITLE = {Integral points and relative sizes of coordinates of orbits in
              {$\mathbb{P}^N$}},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {279},
      YEAR = {2015},
    NUMBER = {3-4},
     PAGES = {1121--1141},
      ISSN = {0025-5874},
   MRCLASS = {37P55 (11J97 37P15)},
  MRNUMBER = {3318263},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.1007/s00209-015-1406-y},
       URL = {http://dx.doi.org/10.1007/s00209-015-1406-y},
}
@article {MR4087476,
    AUTHOR = {Young, Marley},
     TITLE = {On multiplicative independence of rational function iterates},
   JOURNAL = {Monatsh. Math.},
  FJOURNAL = {Monatshefte f\"{u}r Mathematik},
    VOLUME = {192},
      YEAR = {2020},
    NUMBER = {1},
     PAGES = {225--247},
      ISSN = {0026-9255},
   MRCLASS = {11R18 (12E10 37F10 37P05 39B12)},
  MRNUMBER = {4087476},
       DOI = {10.1007/s00605-020-01393-9},
       URL = {https://doi.org/10.1007/s00605-020-01393-9},
}
@comment{UPDATE}
@misc {arxiv2206.14252,
    AUTHOR = {Young, Marley},
    TITLE = {Effective bounds on {$S$}-integral preperiodic points for polynomials},
     YEAR = {2022},
     NOTE = {\url{arXiv:2206.14252}},
}

@article {arxiv0612424,
    AUTHOR = {Yuan, Xinyi},
     TITLE = {Big line bundles over arithmetic varieties},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {173},
      YEAR = {2008},
    NUMBER = {3},
     PAGES = {603--649},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14G40 (11G50 11H06 14C20)},
  MRNUMBER = {MR2425137},
}
@comment{Abstract: We prove a Hilbert-Samuel type result of arithmetic
big line bundles in Arakelov geometry, which is an analogue of a
classical theorem of Siu. An application of this result gives
equidistribution of small points over algebraic dynamical systems,
following the work of Szpiro-Ullmo-Zhang. We also generalize
Chambert-Loir's non-archimedean equidistribution.}

@comment{yuansurvey2010}
@incollection {MR2918034,
    AUTHOR = {Yuan, Xinyi},
     TITLE = {Algebraic dynamics, canonical heights and {A}rakelov geometry},
 BOOKTITLE = {Fifth {I}nternational {C}ongress of {C}hinese
              {M}athematicians. {P}art 1, 2},
    SERIES = {AMS/IP Stud. Adv. Math., 51, pt. 1},
    VOLUME = {2},
     PAGES = {893--929},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2012},
   MRCLASS = {37P15 (11G50 14G40 37P30)},
  MRNUMBER = {2918034},
MRREVIEWER = {J\"{o}rg Jahnel},
}
@misc {arxiv2108.05625,
    AUTHOR = {Yuan, Xinyi},
    TITLE = {Arithmetic bigness and a uniform {B}ogomolov-type result},
     YEAR = {2021},
     NOTE = {\url{arXiv:2108.05625}}
}
@comment{UPDATE}
@misc {yuanzhang09,
    AUTHOR = {Yuan, Xinyi and  Zhang, Shou-Wu},
    TITLE = {Calabi theorem and algebraic dynamics},
     YEAR = {November 14, 2009},
     NOTE = {\url{www.math.harvard.edu/~yxy/preprints/calabisemigroup.pdf}},
}
@comment{UPDATE}
@misc {arXiv2105.13587,
    AUTHOR = {Yuan, Xinyi and  Zhang, Shou-Wu},
    TITLE = {Adelic line bundles over quasi-projective varieties},
     YEAR = {2021},
     NOTE = {\url{arXiv:2105.13587}},
}
@article {MR3090218,
    AUTHOR = {Yurova, E.},
     TITLE = {On ergodicity of {$p$}-adic dynamical systems for arbitrary
              prime {$p$}},
   JOURNAL = {p-Adic Numbers Ultrametric Anal. Appl.},
  FJOURNAL = {p-Adic Numbers, Ultrametric Analysis, and Applications},
    VOLUME = {5},
      YEAR = {2013},
    NUMBER = {3},
     PAGES = {239--241},
      ISSN = {2070-0466},
   MRCLASS = {37P20},
  MRNUMBER = {3090218},
       DOI = {10.1134/S2070046613030072},
       URL = {http://dx.doi.org/10.1134/S2070046613030072},
}
@comment{--ZZZ-- }

@article {MR669663,
    AUTHOR = {Zagier, Don},
     TITLE = {On the number of {M}arkoff numbers below a given bound},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {39},
      YEAR = {1982},
    NUMBER = {160},
     PAGES = {709--723},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {10F20 (10A20 10B10)},
  MRNUMBER = {MR669663 (83k:10062)},
MRREVIEWER = {Richard T. Bumby},
}
@article {MR885780,
    AUTHOR = {Zarhin, Yu. G.},
     TITLE = {Endomorphisms and torsion of abelian varieties},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {54},
      YEAR = {1987},
    NUMBER = {1},
     PAGES = {131--145},
      ISSN = {0012-7094},
   MRCLASS = {14K15 (11G10)},
  MRNUMBER = {885780},
MRREVIEWER = {Ching-li Chai},
       DOI = {10.1215/S0012-7094-87-05410-X},
       URL = {https://doi.org/10.1215/S0012-7094-87-05410-X},
}
@comment{UPDATE}
@misc {arxiv1610.00807,
    AUTHOR = {Zhang, Robin},
    TITLE = {Periodic points of quadratic polynomials in {G}alois extensions},
     YEAR = {2016},
     NOTE = {\url{arXiv:1610.00807}},
}
@comment{UPDATE}
@misc {arxiv2206.09725,
    AUTHOR = {Zhang, Robin},
    TITLE = {The {$abcd$} conjecture, uniform boundedness, and dynamical systems},
     YEAR = {2022},
     NOTE = {\url{arXiv:2206.09725}},
}
@incollection {zhang:distalgdyn,
    AUTHOR = {Zhang, Shou-Wu},
     TITLE = {Distributions in algebraic dynamics},
 BOOKTITLE = {Differential Geometry: A Tribute to Professor {S}.-{S}. {C}hern,
                   Surv. Differ. Geom., Vol. X},
     PAGES = {381--430},
 PUBLISHER = {Int. Press},
   ADDRESS = {Boston, MA},
      YEAR = {2006},
}
@comment{This is an overview of a lot of different topics in
arithmetic dynamics, including canonical metrics, equidistribution of
periodic and small points, dynamical Lehmer and Manin-Mumford
conjectures, etc. There is also a video of a talk by Zhang at MSRI
with this title available at 
www.msri.org/communications/vmath/VMathVideos/VideoInfo/2488/show_video}

@article {MR1609518,
    AUTHOR = {Zhang, Shou-Wu},
     TITLE = {Equidistribution of small points on abelian varieties},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {147},
      YEAR = {1998},
    NUMBER = {1},
     PAGES = {159--165},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {14G40 (11G10 14G05 14K15)},
  MRNUMBER = {MR1609518 (99e:14032)},
MRREVIEWER = {Yuichiro Takeda},
}
@misc {zhang1989unpublished,
    AUTHOR = {Zhang, Shouwu},
    TITLE = {Lower bounds for heights on elliptic curves},
     YEAR = {June 1989},
     NOTE = {\url{unpublished}},
}
@article {MR1311351,
    AUTHOR = {Zhang, Shouwu},
     TITLE = {Small points and adelic metrics},
   JOURNAL = {J. Algebraic Geom.},
  FJOURNAL = {Journal of Algebraic Geometry},
    VOLUME = {4},
      YEAR = {1995},
    NUMBER = {2},
     PAGES = {281--300},
      ISSN = {1056-3911},
   MRCLASS = {14G40},
  MRNUMBER = {1311351 (96e:14025)},
MRREVIEWER = {Antoine Chambert-Loir},
}
@article {MR3976463,
    AUTHOR = {Zhao, Zhengjun and Ji, Qingzhong},
     TITLE = {Zsigmondy theorem for arithmetic dynamics induced by a
              {D}rinfeld module},
   JOURNAL = {Int. J. Number Theory},
  FJOURNAL = {International Journal of Number Theory},
    VOLUME = {15},
      YEAR = {2019},
    NUMBER = {6},
     PAGES = {1111--1125},
      ISSN = {1793-0421},
   MRCLASS = {11G50 (11G09 37F10 37P05)},
  MRNUMBER = {3976463},
MRREVIEWER = {Dragos Ghioca},
       DOI = {10.1142/S1793042119500611},
       URL = {https://doi.org/10.1142/S1793042119500611},
}
@phdthesis{zieve:thesis, 
    AUTHOR = {Zieve, Michael},
    TITLE = {Cycles of Polynomial Mappings},
  SCHOOL  = {University of California at Berkeley},
     YEAR = {1996},
     NOTE = {\url{www.math.rutgers.edu/~zieve/papers/ucthesis.ps}},
}
@comment{UPDATE}
@misc {arxiv1310.0776,
    AUTHOR = {Zieve, Michael},
    TITLE = {A class of permutation trinomials related to {R}edei functions},
     YEAR = {2013},
     NOTE = {\url{arXiv:1310.0776}},
}
@comment{UPDATE}
@misc {arxiv1312.1325,
    AUTHOR = {Zieve, Michael},
    TITLE = {Permutation polynomials induced from permutations of subfields},
     YEAR = {2013},
     NOTE = {\url{arXiv:1312.1325}},
}
@article {MR1875133,
    AUTHOR = {Zilber, Boris},
     TITLE = {Exponential sums equations and the {S}chanuel conjecture},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {65},
      YEAR = {2002},
    NUMBER = {1},
     PAGES = {27--44},
      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {11U09 (03C65 11J99 11L99)},
  MRNUMBER = {MR1875133 (2002m:11104)},
MRREVIEWER = {Ricardo Bianconi},
       DOI = {10.1112/S0024610701002861},
       URL = {http://dx.doi.org/10.1112/S0024610701002861},
}

@article {zimmerman:commpolys,
    AUTHOR = {Zimmerman, Karl},
    TITLE = {Commuting polynomials and self-similarity},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {13},
      YEAR = {2007},
     PAGES = {89--96 (electronic)},
}
@article {MR419455,
    AUTHOR = {Zimmer, Horst G\"{u}nter},
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@comment{zsigmondy}
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@COMMENT{Dynamical degree references added 18 June 2019 ***}

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@comment{UPDATE}
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@COMMENT{Abstract: An N-dimensional diffeomorphism containing a single
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