Tools

LEADER 04350cam 2200589 i 4500

001 on1348498684;

003 OCoLC;

005 20231106090701.0;

008 220811t20222022riua b 001 0 eng ;

010 a| 2022034733;

020 a| 9781470469849q| hardcover;

020 a| 1470469847q| hardcover;

020 a| 9781470472191q| paperback;

020 a| 1470472198q| paperback;

020 z| 9781470472184q| electronic book;

035 a| (Sirsi) o1348498684;

035 a| (OCoLC)1348498684;

042 a| pcc;

049 a| EREE;

050 00 a| QA614.85b| .B78 2022;

082 00 a| 515/.392| 23/eng20221021;

084 a| 37B10a| 37B05a| 28D05a| 11J70a| 68R152| msc;

100 1 a| Bruin, Henk,d| 1966-e| author.=| ^A580819;

245 10 a| Topological and ergodic theory of symbolic dynamics /c| Henk Bruin.;

264 1 a| Providence, Rhode Island :b| American Mathematical Society,c| [2022];

300 a| xvii, 460 pages :b| illustrations ;c| 26 cm.;

336 a| textb| txt2| rdacontent;

337 a| unmediatedb| n2| rdamedia;

338 a| volumeb| nc2| rdacarrier;

490 1 a| Graduate studies in mathematics,x| 1065-7339 ;v| 228;

504 a| Includes bibliographical references (pages 423-450) and index.;

505 0 a| 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.;

520 a| "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."--c| From publisher's website.;

650 0 a| Symbolic dynamics.=| ^A397134;

650 0 a| Topological dynamics.=| ^A18060;

650 0 a| Ergodic theory.=| ^A15765;

650 7 a| Ergodic theory.2| fast0| (OCoLC)fst00914656;

650 7 a| Symbolic dynamics.2| fast0| (OCoLC)fst01140744;

650 7 a| Topological dynamics.2| fast0| (OCoLC)fst01152680;

650 7 a| Dynamical systems and ergodic theory -- Topological dynamics -- Symbolic dynamics.2| msc;

650 7 a| Dynamical systems and ergodic theory -- Topological dynamics -- Transformations and group actions with special properties (minimality, distality, proximality, etc.)2| msc;

650 7 a| Measure and integration -- Measure-theoretic ergodic theory -- Measure-preserving transformations.2| msc;

650 7 a| Number theory -- Diophantine approximation, transcendental number theory -- Continued fractions and generalizations.2| msc;

650 7 a| Computer science -- Discrete mathematics in relation to computer science -- Combinatorics on words.2| msc;

830 0 a| Graduate studies in mathematics ;v| v. 228.=| ^A347883;

994 a| C0b| ERE;

596 a| 1;

998 a| 5953485;

999 a| QA614.85 .B78 2022w| LCc| 1i| 30372017357663d| 5/20/2024e| 8/22/2023l| JGESm| JOYNERr| Ys| Yt| JGESBKu| 1/27/2023x| BOOKz| JSTACKSo| .STAFF. jjlm;

Topological and ergodic theory of symbolic dynamics / Henk Bruin.

Author/creator	Bruin, Henk, 1966- author.
Format	Book
Publication	Providence, Rhode Island : American Mathematical Society, [2022]
Copyright Date	©2022
Description	xvii, 460 pages : illustrations ; 26 cm.
Subjects	Symbolic dynamics. Topological dynamics. Ergodic theory.

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

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Topological and ergodic theory of symbolic dynamics / Henk Bruin.

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