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Topological dimension and dynamical ...

Coornaert, Michel.

Topological dimension and dynamical systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Topological dimension and dynamical systemsby Michel Coornaert.
Author:	Coornaert, Michel.
Published:	Cham :Springer International Publishing :2015.
Description:	xv, 233 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Differentiable dynamical systems.
Online resource:	http://dx.doi.org/10.1007/978-3-319-19794-4
ISBN:	9783319197944 (electronic bk.)

Topological dimension and dynamical systems
Coornaert, Michel.

Topological dimension and dynamical systems[electronic resource] /by Michel Coornaert. - Cham :Springer International Publishing :2015. - xv, 233 p. :ill. (some col.), digital ;24 cm. - 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 Folner'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 (electronic bk.)

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

183764
Differentiable dynamical systems.

LC Class. No.: QA611.5

Dewey Class. No.: 515.39

Topological dimension and dynamical systems
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245 1 0 $a Topological dimension and dynamical systems $h [electronic resource] / $c by Michel Coornaert.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xv, 233 p. : $b ill. (some col.), digital ; $c 24 cm.
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 Folner'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 Differentiable dynamical systems. $3 183764
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
650 2 4 $a Topology. $3 185965
650 0 $a Topological dynamics. $3 468099
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950 $a Mathematics and Statistics (Springer-11649)