國立虎尾科技大學 |

Topological Dimension and Dynamical Systems

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Topological Dimension and Dynamical Systems/ by Michel Coornaert.
Author:	Coornaert, Michel.
Description:	XV, 233 p. 13 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Dynamics. -
Online resource:	https://doi.org/10.1007/978-3-319-19794-4
ISBN:	9783319197944

Topological Dimension and Dynamical Systems
Coornaert, Michel.

Topological Dimension and Dynamical Systems[electronic resource] /by Michel Coornaert. - 1st ed. 2015. - XV, 233 p. 13 illus., 1 illus. in color.online resource. - Universitext,0172-5939. - Universitext,.

Topological Dimension -- Zero-Dimensional Spaces -- Topological Dimension of Polyhedra -- Dimension and Maps -- Some Classical Counterexamples -- Mean Topological Dimension for Continuous Maps -- Shifts and Subshifts over Z -- Applications of Mean Dimension to Embedding Problems -- Amenable Groups -- Mean Topological Dimension for Actions of Amenable Groups.

Translated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts. A large number of revisions and additions have been made to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean topological dimension for continuous actions of countable amenable groups. These new chapters contain material that have never before appeared in textbook form. The chapter on amenable groups is based on Følner’s characterization of amenability and may be read independently from the rest of the book. Although the contents of this book lead directly to several active areas of current research in mathematics and mathematical physics, the prerequisites needed for reading it remain modest; essentially some familiarities with undergraduate point-set topology and, in order to access the final two chapters, some acquaintance with basic notions in group theory. Topological Dimension and Dynamical Systems is intended for graduate students, as well as researchers interested in topology and dynamical systems. Some of the topics treated in the book directly lead to research areas that remain to be explored.

ISBN: 9783319197944

Standard No.: 10.1007/978-3-319-19794-4doiSubjects--Topical Terms:

592238
Dynamics.

LC Class. No.: QA313

Dewey Class. No.: 515.39

Topological Dimension and Dynamical Systems
LDR:03291nam a22004095i 4500 001 965295
003 DE-He213
005 20200705191717.0
007 cr nn 008mamaa
008 201211s2015 gw | s |||| 0|eng d
020 $a 9783319197944 $9 978-3-319-19794-4
024 7 $a 10.1007/978-3-319-19794-4 $2 doi
035 $a 978-3-319-19794-4
050 4 $a QA313
072 7 $a PBWR $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBWR $2 thema
082 0 4 $a 515.39 $2 23
082 0 4 $a 515.48 $2 23
100 1 $a Coornaert, Michel. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1260877
245 1 0 $a Topological Dimension and Dynamical Systems $h [electronic resource] / $c by Michel Coornaert.
250 $a 1st ed. 2015.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a XV, 233 p. 13 illus., 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Universitext, $x 0172-5939
505 0 $a Topological Dimension -- Zero-Dimensional Spaces -- Topological Dimension of Polyhedra -- Dimension and Maps -- Some Classical Counterexamples -- Mean Topological Dimension for Continuous Maps -- Shifts and Subshifts over Z -- Applications of Mean Dimension to Embedding Problems -- Amenable Groups -- Mean Topological Dimension for Actions of Amenable Groups.
520 $a Translated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts. A large number of revisions and additions have been made to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean topological dimension for continuous actions of countable amenable groups. These new chapters contain material that have never before appeared in textbook form. The chapter on amenable groups is based on Følner’s characterization of amenability and may be read independently from the rest of the book. Although the contents of this book lead directly to several active areas of current research in mathematics and mathematical physics, the prerequisites needed for reading it remain modest; essentially some familiarities with undergraduate point-set topology and, in order to access the final two chapters, some acquaintance with basic notions in group theory. Topological Dimension and Dynamical Systems is intended for graduate students, as well as researchers interested in topology and dynamical systems. Some of the topics treated in the book directly lead to research areas that remain to be explored.
650 0 $a Dynamics. $3 592238
650 0 $a Ergodic theory. $3 672355
650 0 $a Topology. $3 633483
650 1 4 $a Dynamical Systems and Ergodic Theory. $3 671353
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319197951
776 0 8 $i Printed edition: $z 9783319197937
830 0 $a Universitext, $x 0172-5939 $3 1253835
856 4 0 $u https://doi.org/10.1007/978-3-319-19794-4
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)