The Arithmetic of Dynamical Systems

1. Auflage. Softcover version of original hardcover Auflage 2007
ISBN: 978-1-4419-2417-9
Verlag: Springer

Buch, Englisch, 511 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 791 g

Reihe: Graduate Texts in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Silverman, J. H.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

An Introduction to Classical Dynamics.- Dynamics over Local Fields: Good Reduction.- Dynamics over Global Fields.- Families of Dynamical Systems.- Dynamics over Local Fields: Bad Reduction.- Dynamics Associated to Algebraic Groups.- Dynamics in Dimension Greater Than One.