Symbolic Dynamics

One-sided, Two-sided and Countable State Markov Shifts

AvBruce P. Kitchens

Häftad, Engelska, 1997

Del i serien Universitext

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Beskrivning

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 established using elementary methods. The connections to other types of dynamical systems, cellular automata and information theory are illustrated with numerous examples. The book is written for graduate students and others who use symbolic dynamics as a tool to study more general systems.

Produktinformation

Utgivningsdatum:1997-11-14
Mått:155 x 235 x 15 mm
Vikt:411 g
Format:Häftad
Språk:Engelska
Serie:Universitext
Antal sidor:254
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540627388

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Tillämpad matematik inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Recensioner i media

"...a clear and efficient treatment of an intrinsically interesting subject and would be a valuable addition to any dynamicists mathematical library." - UK Nonlinear News

Innehållsförteckning

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.