Dynamical systems and ergodic theory / Mark Pollicott, Michiko Yuri.

Format:

Book

Author/Creator:

Pollicott, Mark, author.

Yuri, Michiko, 1956- author.

Series:

London Mathematical Society student texts ; 40.

London Mathematical Society student texts ; 40

Language:

English

Subjects (All):

Topological dynamics.

Ergodic theory.

Physical Description:

1 online resource (xiii, 179 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1998.

Language Note:

English

Summary:

Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory.

Contents:

Cover; Series Page; Title; Copyright; CONTENTS; INTRODUCTION; PRELIMINARIES; 1 Conventions; 2 Notation; 3 Prerequisites in point set topology (CHAPTERs 1-6); 4 Pre-requisites in measure theory (CHAPTERs 7-12); 5 Subadditive sequences; References; CHAPTER 1 EXAMPLES AND BASIC PROPERTIES; 1.1 Examples; 1.2 Transitivity; 1.3 Other characterizations of transitivity; 1.4 Transitivity for subshifts of finite type; 1.5 Minimality and the Birkhoff recurrence theorem; 1.6 Commuting homeomorphisms; 1.7 Comments and references; References

CHAPTER 2 AN APPLICATION OF RECURRENCE TO ARITHMETIC PROGRESSIONS2.1 Van der Waerden's theorem; 2.2 A dynamical proof; 2.3. The proofs of Sublemma 2.2.2 and Sublemma 2.2.3; 2.4 Comments and references; References; CHAPTER 3 TOPOLOGICAL ENTROPY; 3.1 Definitions; 3.2 The Perron-Frobenious theorem and subshifts of finite type; 3.3 Other definitions and examples; 3.4 Conjugacy; 3.5 Comments and references; References; CHAPTER 4 INTERVAL MAPS; 4.1 Fixed points and periodic points; 4.2 Topological entropy of interval maps; 4.3 Markov maps; 4.4 Comments and references; References

CHAPTER 5 HYPERBOLIC TORAL AUTOMORPHISMS5.1 Definitions; 5.2 Entropy for Hyperbolic Toral Automorphisms; 5.3 Shadowing and semi-conjugacy; 5.4 Comments and references; References; CHAPTER 6 ROTATION NUMBERS; 6.1 Homeomorphisms of the circle and rotation numbers; 6.2 Denjoy's theorem; 6.3 Comments and references; References; CHAPTER 7 INVARIANT MEASURES; 7.1 Definitions and characterization of invariant measures; 7.2 Borel sigma-algebras for compact metric spaces; 7.3 Examples of invariant measures; 7.4 Invariant measures for other actions; 7.5 Comments and references; References

CHAPTER 8 MEASURE THEORETIC ENTROPY8.1 Partitions and conditional expectations; 8.2 The entropy of a partition; 8.3 The entropy of a transformation; 8.4 The increasing martingale theorem; 8.5 Entropy and sigma-algebras; 8.6 Conditional entropy; 8.7 Proofs of Lemma 8.7 and Lemma 8.8; 8.8 Isomorphism; 8.9 Comments and references; References; CHAPTER 9 ERGODIC MEASURES; 9.1 Definitions and characterization of ergodic measures; 9.2 Poincare recurrence and Kac's theorem; 9.3 Existence of ergodic measures; 9.4 Some basic constructions in ergodic theory; 9.4.1 Skew products

9.4.2 Induced transformations and Rohlin towers9.4.3 Natural extensions; 9.5 Comments and references; References; CHAPTER 10 ERGODIC THEOREMS; 10.1 The Von Neumann ergodic theorem; 10.2 The Birkhoff theorem (for ergodic measures); 10.3 Applications of the ergodic theorems; 10.4 The Birkhoff theorem (for invariant measures); 10.5 Comments and references; References; CHAPTER 11 MIXING PROPERTIES; 11.1 Weak mixing; 11.2 A density one convergence characterization of weak mixing; 11.3 A generalization of the von Neumann ergodic theorem; 11.4 The spectral viewpoint

11.5 Spectral characterization of weak mixing

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-316-08743-3

1-139-17304-9

1-107-09188-8

1-107-08895-X

1-107-10079-8

1-107-09514-X

OCLC:

853360446