Symbolic Dynamics One-sided, Two-sided and Countable State Markov Shifts
This is a thorough introduction to the dynamics of one-sided and two-sided Markov shifts on a finite alphabet and to the basic properties of Markov shifts on a countable alphabet. These are the symbolic dynamical systems defined by a finite transition rule. The basic properties of these systems are...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1998, 1998
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| Edition: | 1st ed. 1998 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Background and Basics
- § 1.1 Subshifts of Finite Type
- § 1.2 Examples
- § 1.3 Perron-Frobenius Theory
- § 1.4 Basic Dynamics
- Notes
- References
- 2. Topology Conjugacy
- § 2.1 Decomposition of Topological Conjugacies
- § 2.2 Algebraic Consequences of Topological Conjugacy
- Notes
- References
- 3. Automorphisms
- § 3.1 Automorphisms
- § 3.2 Automorphisms as Conjugacies
- § 3.3 Subgroups of the Automorphism Group
- § 3.4 Actions of Automorphisms
- § 3.5 Summary
- Notes
- References
- 4. Embeddinggs and Factor Maps
- § 4.1 Factor Maps
- § 4.2 Finite-to-one Factor Maps
- §4.3 Special Constructions Involving Factor Maps
- § 4.4 Subsystems and Infinite-to-One Factor Maps
- Notes
- References
- 5. Almost-Topological Conjugacy
- § 5.1 Reducible Subshifts of Finite Type
- § 5.2 Almost-Topological Conjugacy
- Notes
- References
- 6. Further Topics
- § 6.1 Sofic Systems
- § 6.2 Markov Measures and the Maximal Measure
- § 6.3 Markov Subgroups
- § 6.4 Cellular Automata
- § 6.5 Channnel Codes
- Notes
- References
- 7. Countable State Markov Shifts
- § 7.1 Perron-Frobenius Theory
- § 7.2 Basic Symbolic Dynamics
- Notes
- References
- Name Index