Topological and ergodic theory of symbolic dynamics / Henk Bruin.

• First examples and general properties of subshifts -- Topological dynamics -- Subshifts of positive entropy -- Subshifts of zero entropy -- Further minimal Cantor systems -- Methods from ergodic theory -- Automata and linguistic complexity -- Miscellaneous background topics.

• "Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, B-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book."-- 

Ämnesord

Ergodisk teori  (sao)

Symbolic dynamics.  (LCSH)

Topological dynamics.  (LCSH)

Ergodic theory.  (fast)

Symbolic dynamics.  (fast)

Topological dynamics.  (fast)

Dynamical systems and ergodic theory -- Topological dynamics -- Symbolic dynamics.  (msc)

Dynamical systems and ergodic theory -- Topological dynamics -- Transformations and group actions with special properties (minimality, distality, proximality, etc.).  (msc)

Measure and integration -- Measure-theoretic ergodic theory -- Measure-preserving transformations.  (msc)

Number theory -- Diophantine approximation, transcendental number theory -- Continued fractions and generalizations.  (msc)

Computer science -- Discrete mathematics in relation to computer science -- Combinatorics on words.  (msc)

Ergodic theory  (LCSH)

Klassifikation

QA614.85 (LCC)

515/.39 (DDC)

37B10 (msc)

Tdcb (kssb/8 (machine generated))