# The Arithmetic of Dynamical Systems

@inproceedings{Silverman2007TheAO,
title={The Arithmetic of Dynamical Systems},
author={Joseph H. Silverman},
year={2007}
}
* Provides an entry for graduate students into an active field of research * Each chapter includes exercises, examples, and figures * Will become a standard reference for researchers in the field * Contains descriptions of many known results and conjectures, together with an extensive bibliography This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real…
577 Citations
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A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: for any prime $p$, reduce its coefficients mod $p$ and consider its action on the field $Examples of dynamical degree equals arithmetic degree • Mathematics • 2012 Let f : X --> X be a dominant rational map of a projective variety defined over a number field. An important geometric-dynamical invariant of f is its (first) dynamical degree d_f= lim Heights on moduli space for post-critically finite dynamical systems The purpose of this Research In Teams event was to consider the arithmetic properties of post-critically finite (PCF) rational maps. In the study of complex holomorphic dynamics, it is a general ## References SHOWING 1-10 OF 53 REFERENCES S-integer dynamical systems: periodic points. • Mathematics • 1997 We associate via duality a dynamical system to each pair (RS,x), where RS is the ring of S-integers in an A-field k, and x is an element of RS\{0}. These dynamical systems include the circle doubling Homoclinic points of algebraic ℤ^{}-actions • Mathematics • 1999 An algebraic zd-action is an action of Zd by (continuous) automorphisms of a compact abelian group. The dynamics of a single group automorphism have been investigated in great detail over the past Advanced Topics in the Arithmetic of Elliptic Curves In The Arithmetic of Elliptic Curves, the author presented the basic theory culminating in two fundamental global results, the Mordell-Weil theorem on the finite generation of the group of rational Almost all$S$-integer dynamical systems have many periodic points • T. Ward • Mathematics Ergodic Theory and Dynamical Systems • 1998 We show that for almost every ergodic$S$-integer dynamical system the radius of convergence of the dynamical zeta function is no larger than$\exp(-\frac{1}{2}h_{\rm top})<1\$. In the arithmetic case
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Institute for Mathematical Physics Expansive Subdynamics for Algebraic Z D {actions Expansive Subdynamics for Algebraic Z D -actions
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Institute for Mathematical Physics Homoclinic Points of Algebraic Z D {actions Homoclinic Points of Algebraic Z D -actions
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• 1996
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