Dynamical Systems and Ergodic Theory: 40 (London Mathematical Society Student Texts, Series Number 40)
Cambridge University Press, 1/29/1998
EAN 9780521572941, ISBN10: 0521572940
Hardcover, 196 pages, 23.6 x 15.7 x 1.8 cm
Language: English
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.