The Arithmetic of Dynamical Systems
Joseph H. Silverman
Springer-Verlag – Graduate Texts in Mathematics 241
ISBN: 13: 978-0-387-69903-5
– 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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