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Arithmetic of Dynamical Systems

Arithmetic of Dynamical Systems - 07 edition

Arithmetic of Dynamical Systems - 07 edition

ISBN13: 9780387699035

ISBN10: 0387699031

Arithmetic of Dynamical Systems by Joseph H. Silverman - ISBN 9780387699035
Edition: 07
Copyright: 2007
Publisher: Springer
Published:
International: No
Arithmetic of Dynamical Systems by Joseph H. Silverman - ISBN 9780387699035

ISBN13: 9780387699035

ISBN10: 0387699031

Edition: 07

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Summary

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.