The Arithmetic of Dynamical Systems
Joseph H. Silverman
SpringerVerlag – Graduate Texts in Mathematics 241
ISBN: 13: 9780387699035
– 1st ed.
– © 2007
– 511 + ix pages
Math. Subj. Class [2010]: 37Pxx (37P05, 37P15, 37P20, 37P30, 37P35, 37P45, 37P50)
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The Arithmetic of Dynamical Systems is a graduate level text
designed to provide an entry into a new field that is an amalgamation
of two venerable areas of mathematics, Dynamical Systems and Number
Theory. Many of the motivating theorems and conjectures in the new
subject of Arithmetic Dynamics may be viewed as the transposition of
classical results in the theory of Diophantine equations to the
setting of discrete dynamical systems, especially to the iteration
theory of maps on the projective line and other algebraic
varieties.
Contents
 An Introduction to Classical Dynamics
 Dynamics Over Local Fields: Good Reduction
 Dynamics Over Global Fields
 Families of Dynamical Systems
 Dynamics Over Local Fields: Bad Reduction
 Dynamics Associated to Algebraic Groups
 Dynamics in Dimension Greater Than One
Click on the links for the following material.
Errata List

No book is ever free from error or incapable of being improved. I
would be delighted to receive comments, good or bad, and corrections
from my readers. You can send mail to me at
jhs@math.brown.edu
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