Screen LibraryThe arithmetic of dynamical systems
Saved in:
| Main Authors: | |
|---|---|
| Corporate Authors: | |
| Published: |
Springer,
|
| Publisher Address: | New York |
| Publication Dates: | 2007. |
| Literature type: | Book |
| Language: | English |
| Series: |
Graduate texts in mathematics ; 241 |
| Subjects: | |
| Online Access: |
http://dx.doi.org/10.1007/978-0-387-69904-2 |
| Carrier Form: | 1 online resource (ix, 511 p.): ill. |
| ISBN: |
9780387699042 (electronic bk.) 038769904X (electronic bk.) |
| Index Number: | O193 |
| CLC: | O193-43 |
| Contents: |
Textbook for graduates. Includes bibliographical references (p. 451-471) and index. 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. 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. |