Classification Problems in Ergodic Theory /

Classification Problems in Ergodic Theory / William Parry, Selim Tuncel.

Lecturers and postgraduates in mathematics and research workers in communication engineering will find this book of use and interest.

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Bibliographic Details
Online Access: Full Text (via Cambridge)
Other Authors: Parry, William, 1934-2006, Tuncel, Selim
Format: Electronic eBook
Language:English
Published: Cambridge : Cambridge University Press, 1982.
Series:London Mathematical Society lecture note series ; no. 67.
Subjects:
Ergodic theory.
Isomorphisms (Mathematics)
Table of Contents:
  • Cover
  • Title
  • Copyright
  • Contents
  • Preface
  • Chapter I: Introduction
  • 1. Motivation
  • 2. Basic Definitions and Conventions
  • 3. Processes
  • 4. Markov Chains
  • 5. Reduced Processes and Topological Markov Chains
  • 6. Information and Entropy
  • 7. Types of Classification
  • Chapter II: The Information Cocycle
  • 1. Regular Isomorphisms
  • 2. Unitary Operators and Cocycles
  • 3. Information Variance
  • 4. The Variational Principle for Topological Markov Chains
  • 5. A Group Invariant.
  • 6. Quasi-regular Isomorphisms and Bounded Codes
  • 7. Central Limiting Distributions as Invariants
  • Chapter III: Finitary Isomorphisms
  • 1. The Marker Method
  • 2. Finite Expected Code-lengths
  • Chapter IV: Block-codes
  • 1. Continuity and Block-codes
  • 2. Bounded-to-one Codes
  • 3. Suspensions and Winding Numbers
  • 4. Computation of the First Cohomology Group
  • Chapter V: Classifications of Topological Markov Chains
  • 1. Finite Equivalence
  • 2. Almost Topological Conjugacy and the Road Problem.
  • 3. Topological Conjugacy of Topological Markov Chains
  • 4. Invariants and Reversibility
  • 5. Flow Equivalence
  • Appendix: Shannon's Work on Maximal Measures
  • References
  • Index.

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