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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 |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1982.
|
| Colección: | London Mathematical Society lecture note series ;
67. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Parry, William, |d 1934-2006. | |
| 245 | 1 | 0 | |a Classification problems in ergodic theory / |c William Parry and Selim Tuncel. |
| 260 | |a Cambridge [Cambridgeshire] ; |a New York : |b Cambridge University Press, |c 1982. | ||
| 300 | |a 1 online resource (101 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society lecture note series, |x 0076-0552 ; |v 67 | |
| 504 | |a Includes bibliographical references (pages 96-99) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Ergodic theory. | |
| 650 | 0 | |a Isomorphisms (Mathematics) | |
| 650 | 6 | |a Théorie ergodique. | |
| 650 | 6 | |a Isomorphismes (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Ergodic theory |2 fast | |
| 650 | 7 | |a Isomorphisms (Mathematics) |2 fast | |
| 650 | 7 | |a Ergodentheorie |2 gnd | |
| 650 | 7 | |a Théorie ergodique. |2 ram | |
| 650 | 7 | |a Isomorphismes (mathématiques) |2 ram | |
| 700 | 1 | |a Tuncel, Selim. | |
| 776 | 0 | 8 | |i Print version: |a Parry, William, 1934-2006. |t Classification problems in ergodic theory. |d Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1982 |z 0521287944 |w (DLC) 82004350 |w (OCoLC)8388077 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 67. |x 0076-0552 | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552523 |z Texto completo |
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