The Arithmetic of Dynamical Systems

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

Buch, Englisch, Band 241, 511 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 791 g

Reihe: Graduate Texts in Mathematics

This book investigates the relatively new subject of Arithmetic Dynamics, which is the study of the number theoretic properties of algebraic numbers or points under repeated application of a polynomial or rational map. Classical discrete dynamics is the study of iteration of functions mapping the complex plane (or real line) to itself. Arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. The viewpoint of this book 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, an overarching theme is that at least qualitatively, the geometry determines the arithmetic.

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.