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).Read more
- Few other books on this subject
- Perfect for a master's course
- Authors are well known in this area
Reviews & endorsements
' … 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
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- Date Published: January 1998
- format: Paperback
- isbn: 9780521575997
- length: 196 pages
- dimensions: 228 x 151 x 13 mm
- weight: 0.275kg
- availability: Available
Table of Contents
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
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.
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