Dynamical systems and ergodic theory
著者
書誌事項
Dynamical systems and ergodic theory
（London Mathematical Society student texts, 40）
Cambridge University Press, 1998
- : hbk
- : pbk
大学図書館所蔵 全67件
注記
Includes bibliographical references and index
内容説明・目次
内容説明
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).
目次
- 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.
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