Topological and ergodic theory of symbolic dynamics / Henk Bruin.

Format:

Book

Author/Creator:

Bruin, Henk, 1966- author.

Series:

Graduate studies in mathematics ; 1065-7339 228.

Graduate studies in mathematics, 1065-7339 ; 228

Language:

English

Subjects (All):

Symbolic dynamics.

Topological dynamics.

Ergodic theory.

Physical Description:

xvii, 460 pages : illustrations ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2022]

Summary:

"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."-- From publisher's website.

Contents:

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.

Notes:

Includes bibliographical references (pages 423-450) and index.

Other Format:

Online version: Bruin, Henk, 1966- Topological and ergodic theory of symbolic dynamics.

ISBN:

9781470469849

1470469847

9781470472191

1470472198

OCLC:

1348498684