Bruce P. Kitchens

Symbolic Dynamics (eBook, PDF)

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

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 254
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642588228
• Artikelnr.: 53379870

Inhaltsangabe

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.

Rezensionen

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