國立虎尾科技大學 |

Ergodic theory and dynamical systems

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Ergodic theory and dynamical systems/ by Yves Coudene ; translated by Reinie Erne.
Author:	Coudene, Yves.
other author:	Erne, Reinie.
Published:	London :Springer London : : 2016.,
Description:	xiii, 190 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Ergodic theory. -
Online resource:	http://dx.doi.org/10.1007/978-1-4471-7287-1
ISBN:	9781447172871

Ergodic theory and dynamical systems
Coudene, Yves.

Ergodic theory and dynamical systems[electronic resource] /by Yves Coudene ; translated by Reinie Erne. - London :Springer London :2016. - xiii, 190 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

Introduction -- Part I Ergodic Theory -- The Mean Ergodic Theorem -- The Pointwise Ergodic Theorem -- Mixing -- The Hopf Argument -- Part II Dynamical Systems -- Topological Dynamics -- Nonwandering -- Conjugation -- Linearization -- A Strange Attractor -- Part III Entropy Theory -- Entropy -- Entropy and Information Theory -- Computing Entropy -- Part IV Ergodic Decomposition -- Lebesgue Spaces and Isomorphisms -- Ergodic Decomposition -- Measurable Partitions and -Algebras -- Part V Appendices -- Weak Convergence -- Conditional Expectation -- Topology and Measures -- References.

This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.

ISBN: 9781447172871

Standard No.: 10.1007/978-1-4471-7287-1doiSubjects--Topical Terms:

672355
Ergodic theory.

LC Class. No.: QA313

Dewey Class. No.: 515.48

Ergodic theory and dynamical systems
LDR:02699nam a2200337 a 4500 001 868274
003 DE-He213
005 20161111101439.0
006 m d
007 cr nn 008maaau
008 170720s2016 enk s 0 eng d
020 $a 9781447172871 $q (electronic bk.)
020 $a 9781447172857 $q (paper)
024 7 $a 10.1007/978-1-4471-7287-1 $2 doi
035 $a 978-1-4471-7287-1
040 $a GP $c GP
041 1 $a eng $h fre
050 4 $a QA313
072 7 $a PBWR $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 515.48 $2 23
090 $a QA313 $b .C854 2016
100 1 $a Coudene, Yves. $3 1115788
240 1 0 $a Theorie ergodique er systemes dynamiques. $l English
245 1 0 $a Ergodic theory and dynamical systems $h [electronic resource] / $c by Yves Coudene ; translated by Reinie Erne.
260 $a London : $c 2016. $b Springer London : $b Imprint: Springer,
300 $a xiii, 190 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 0172-5939
505 0 $a Introduction -- Part I Ergodic Theory -- The Mean Ergodic Theorem -- The Pointwise Ergodic Theorem -- Mixing -- The Hopf Argument -- Part II Dynamical Systems -- Topological Dynamics -- Nonwandering -- Conjugation -- Linearization -- A Strange Attractor -- Part III Entropy Theory -- Entropy -- Entropy and Information Theory -- Computing Entropy -- Part IV Ergodic Decomposition -- Lebesgue Spaces and Isomorphisms -- Ergodic Decomposition -- Measurable Partitions and -Algebras -- Part V Appendices -- Weak Convergence -- Conditional Expectation -- Topology and Measures -- References.
520 $a This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.
650 0 $a Ergodic theory. $3 672355
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
700 1 $a Erne, Reinie. $3 1115789
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Universitext. $3 881573
856 4 0 $u http://dx.doi.org/10.1007/978-1-4471-7287-1
950 $a Mathematics and Statistics (Springer-11649)