Symbolic dynamics : one-sided, two-sided and countable state Markov shifts

Bruce P. Kitchens

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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[目次]

  • 1. Background and Basics.- x 1.1 Subshifts of Finite Type.- x 1.2 Examples.- x 1.3 Perron-Frobenius Theory.- x 1.4 Basic Dynamics.- Notes.- References.- 2. Topology Conjugacy.- x 2.1 Decomposition of Topological Conjugacies.- x 2.2 Algebraic Consequences of Topological Conjugacy.- Notes.- References.- 3. Automorphisms.- x 3.1 Automorphisms.- x 3.2 Automorphisms as Conjugacies.- x 3.3 Subgroups of the Automorphism Group.- x 3.4 Actions of Automorphisms.- x 3.5 Summary.- Notes.- References.- 4. Embeddinggs and Factor Maps.- x 4.1 Factor Maps.- x 4.2 Finite-to-one Factor Maps.- x4.3 Special Constructions Involving Factor Maps.- x 4.4 Subsystems and Infinite-to-One Factor Maps.- Notes.- References.- 5. Almost-Topological Conjugacy.- x 5.1 Reducible Subshifts of Finite Type.- x 5.2 Almost-Topological Conjugacy.- Notes.- References.- 6. Further Topics.- x 6.1 Sofic Systems.- x 6.2 Markov Measures and the Maximal Measure.- x 6.3 Markov Subgroups.- x 6.4 Cellular Automata.- x 6.5 Channnel Codes.- Notes.- References.- 7. Countable State Markov Shifts.- x 7.1 Perron-Frobenius Theory.- x 7.2 Basic Symbolic Dynamics.- Notes.- References.- Name Index.

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この本の情報

書名 Symbolic dynamics : one-sided, two-sided and countable state Markov shifts
著作者等 Kitchens, Bruce
Kitchens Bruce P.
書名別名 Symbolic dynamics
シリーズ名 Universitext
出版元 Springer
刊行年月 c1998
版表示 Softcover reprint of the original 1st ed. 1998
ページ数 x, 252 p.
大きさ 24 cm
ISBN 3540627383
NCID BA33505720
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言語 英語
出版国 ドイツ
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