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Book Cover
E-book
Author Parry, William, 1934-2006.

Title Classification problems in ergodic theory / William Parry and Selim Tuncel
Published Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1982

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Description 1 online resource (101 pages) : illustrations
Series London Mathematical Society lecture note series, 0076-0552 ; 67
London Mathematical Society lecture note series ; 67. 0076-0552
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 Method2. 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
Summary The isomorphism problem of ergodic theory has been extensively studied since Kolmogorov's introduction of entropy into the subject and especially since Ornstein's solution for Bernoulli processes. Much of this research has been in the abstract measure-theoretic setting of pure ergodic theory. However, there has been growing interest in isomorphisms of a more restrictive and perhaps more realistic nature which recognize and respect the state structure of processes in various ways. These notes give an account of some recent developments in this direction. A special feature is the frequent use of the information function as an invariant in a variety of special isomorphism problems. Lecturers and postgraduates in mathematics and research workers in communication engineering will find this book of use and interest
Bibliography Includes bibliographical references (pages 96-99) and index
Notes Print version record
Subject Ergodic theory.
Isomorphisms (Mathematics)
MATHEMATICS -- Calculus.
MATHEMATICS -- Mathematical Analysis.
Ergodic theory
Isomorphisms (Mathematics)
Ergodentheorie
Théorie ergodique.
Isomorphismes (mathématiques)
Form Electronic book
Author Tuncel, Selim
ISBN 9781107361201
1107361206
9780511892165
0511892160