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Classification problems in ergodic theory /
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 theo...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1982.
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| Colección: | London Mathematical Society lecture note series ;
67. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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