Dynamical Systems and Ergodic Theory

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Mark Pollicott (University of Manchester) Michiko Yuri (Sapporo University, Japan)

Dynamical Systems and Ergodic Theory

Mark Pollicott (University of Manchester), Michiko Yuri (Sapporo University, Japan)

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English

Cambridge University Press
30 March 1998

Calculus & mathematical analysis; Analytic topology

Series: London Mathematical Society Student Texts

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).

By: Mark Pollicott (University of Manchester), Michiko Yuri (Sapporo University, Japan)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 40
Dimensions: Height: 236mm, Width: 157mm, Spine: 18mm
Weight: 390g
ISBN: 9780521572941
ISBN 10: 0521572940
Series: London Mathematical Society Student Texts
Pages: 196
Publication Date: 30 March 1998
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Reviews for Dynamical Systems and Ergodic Theory

' … 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