Topological and ergodic theory of symbolic dynamics / Henk Bruin.
| Author/creator |
Bruin, Henk, 1966- author. |
| Format | Book and Print |
| Publication Info | Providence, Rhode Island : American Mathematical Society, [2022] |
| Copyright Notice | ©2022 |
| Description | xvii, 460 pages : illustrations ; 26 cm. |
| Subject(s) |
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| Series | Graduate studies in mathematics, 1065-7339 ; 228 Graduate studies in mathematics ; v. 228. ^A347883 |
| 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. |
| Abstract | "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. |
| Bibliography note | Includes bibliographical references (pages 423-450) and index. |
| Issued in other form | Online version: Bruin, Henk, 1966- Topological and ergodic theory of symbolic dynamics. Providence, Rhode Island : American Mathematical Society, [2022] 9781470472184 |
| LCCN | 2022034733 |
| ISBN | 9781470469849 hardcover |
| ISBN | 1470469847 hardcover |
| ISBN | 9781470472191 paperback |
| ISBN | 1470472198 paperback |
| ISBN | electronic book |
Available Items
| Library | Location | Call Number | Status | Item Actions | |
| Joyner | General Stacks | QA614.85 .B78 2022 | ✔ Available | Place Hold |