Dynamical Systems and Ergodic Theory

Dynamical Systems and Ergodic Theory

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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).show more

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' ... 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 Newsshow more

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.show more

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