Classification problems in ergodic theory

Cover......Page 1
Title Page......Page 4
Copyright......Page 5
CONTENTS......Page 6
Preface......Page 8
1. Motivation......Page 10
2. Basic Definitions and Conventions......Page 11
3. Processes......Page 12
4. Markov Chains......Page 13
5. Reduced Processes and Topological Markov Chains......Page 14
6. Information and Entropy......Page 16
7. Types of Classification......Page 19
1. Regular Isomorphisms......Page 21
2. Unitary Operators and Cocycles......Page 23
3. Information Variance......Page 27
4. The Variational Principle for Topological Markov Chains......Page 30
5. A Group Invariant......Page 35
6. Quasi-regular Isomorphisms and Bounded Codes......Page 40
7. Central Limiting Distributions as Invariants......Page 45
1. The Marker Method......Page 47
2. Finite Expected Code-lengths......Page 59
1. Continuity and Block-codes......Page 63
2. Bounded-to-one Codes......Page 65
3. Suspensions and Winding Numbers......Page 68
4. Computation of the First Cohomology Group......Page 71
1. Finite Equivalence......Page 73
2. Almost Topological Conjugacy and the Road Problem......Page 78
3. Topological Conjugacy of Topological Markov Chains......Page 81
4. Invariants and Reversibility......Page 88
5. Flow Equivalence......Page 92
Appendix: Shannon\'s Work on Maximal Measures......Page 99
References......Page 105
Index......Page 109