Overview

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 line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.

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<p>From the reviews: <p> The connections between dynamical systems and number theory arise in many different ways. This remarkable book unifies and clarifies one of these connections, in the setting of what might be called Arithmetic Dynamical Systems . suitable for many graduate students. This book should be of great interest to anyone interested in dynamics or number theory, and will attract them into this fascinating field. Not for the first time, the mathematical community owes the author thanks for a wonderful book . (Thomas Ward, Mathematical Reviews, Issue 2008 c)<p> The Arithmetic of Dynamical Systems is intended for an audience of researchers and graduate students in number theory. The book could easily be used for a special-topics graduate course. will serve not only as an excellent introduction to the Diophantine aspects of dynamics for the uninitiated, but also as a valuable reference for experts in the field. It is certain to be an essential resource for anyone interes

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