The Arithmetic of Dynamical Systems

• Main Author: Silverman, Joseph H. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2007.
• Series: Graduate Texts in Mathematics, 241
• Subjects: Mathematics.; Data structures (Computer science).; Dynamics.; Ergodic theory.; Dynamical Systems and Ergodic Theory.; Data Structures.

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 poin...

Table of Contents:

• 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.