The Arithmetic of Dynamical Systems

  • Joseph H. Silverman

Part of the Graduate Texts in Mathematics book series (GTM, volume 241)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Joseph H. Silverman
    Pages 1-8
  3. Joseph H. Silverman
    Pages 9-41
  4. Joseph H. Silverman
    Pages 43-79
  5. Joseph H. Silverman
    Pages 81-146
  6. Joseph H. Silverman
    Pages 147-237
  7. Joseph H. Silverman
    Pages 239-324
  8. Joseph H. Silverman
    Pages 325-385
  9. Joseph H. Silverman
    Pages 387-439
  10. Back Matter
    Pages 441-515

About this book


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. As is typical in any subject combining Diophantine problems and geometry, a fundamental goal is to describe arithmetic properties, at least qualitatively, in terms of underlying geometric structures.

Key features:

- Provides an entry for graduate students into an active field of research

- Provides a standard reference source for researchers

- Includes numerous exercises and examples

- Contains a description of many known results and conjectures, as well as an extensive glossary, bibliography, and index

This graduate-level text assumes familiarity with basic algebraic number theory. Other topics, such as basic algebraic geometry, elliptic curves, nonarchimedean analysis, and the theory of Diophantine approximation, are introduced and referenced as needed. Mathematicians and graduate students will find this text to be an excellent reference.


Dimension Diophantine approximation Grad algebraic geometry algebraic group dynamical systems geometry number theory

Authors and affiliations

  • Joseph H. Silverman
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 2007
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-69903-5
  • Online ISBN 978-0-387-69904-2
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site