Dynamical Systems and Ergodic Theory

Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory.

Mark Pollicott (Author), Michiko Yuri (Author)

9780521572941, Cambridge University Press

Hardback, published 29 January 1998

196 pages
23.6 x 15.7 x 1.8 cm, 0.39 kg

' … the volume achieves its goals well. It covers a broad range of topics clearly and succinctly … There is much material here to interest and stimulate the reader … I thoroughly recommend it to anyone of has some knowledge of the subject matter and wants a concise and well presented reference for more advanced concepts.' UK Non-Linear News

This book is essentially a self-contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a master's level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der Waerden's theorem and Szemerdi's theorem).

Introduction and preliminaries
Part I. Topological Dynamics: 1. Examples and basic properties
2. An application of recurrence to arithmetic progressions
3. Topological entropy
4. Interval maps
5. Hyperbolic toral automorphisms
6. Rotation numbers
Part II. Measurable Dynamics: 7. Invariant measures
8. Measure theoretic entropy
9. Ergodic measures
10. Ergodic theorems
11. Mixing
12. Statistical properties
Part III. Supplementary Chapters: 13. Fixed points for the annulus
14. Variational principle
15. Invariant measures for commuting transformations
16. An application of ergodic theory to arithmetic progressions.

Subject Areas: Calculus & mathematical analysis [PBK]