Dynamical Systems and Ergodic Theory
Dynamical Systems and Ergodic Theory
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This book is an 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. The authors provide a number of applications, principally to number theory and arithmetic progressions (through Van der Waerden's theorem and Szemerdi's theorem). This text is suitable for advanced undergraduate and beginning graduate students.
- 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
Product details
February 1998Hardback
9780521572941
196 pages
236 × 157 × 18 mm
0.39kg
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
- 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.
