The Arithmetic of Dynamical Systems

Joseph H. Silverman - Collection Graduate Texts in Mathematics

512 pages, parution le 01/06/2007

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Résumé

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.

Written for:

Mathematicians and graduate students

Sommaire

Preface
An Introduction to Classical Dynamics
Dynamics over Local Fields: Good Reduction
Dynamics over Global Fields
Dynamics and Moduli
Dynamics over Local Fields: Bad Reduction
Dynamics with an Underlying Group
Dynamics in Dimension Greater than One

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Joseph H. Silverman
Collection	Graduate Texts in Mathematics
Parution	01/06/2007
Nb. de pages	512
Couverture	Relié
Intérieur	Noir et Blanc
EAN13	9780387699035
ISBN13	978-0-387-69903-5