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An introduction to the Kolmogorov-Be...

Ponce, Gabriel.

An introduction to the Kolmogorov-Bernoulli equivalence

Record Type:	Electronic resources : Monograph/item
Title/Author:	An introduction to the Kolmogorov-Bernoulli equivalenceby Gabriel Ponce, Regis Varao.
Author:	Ponce, Gabriel.
other author:	Varao, Regis.
Published:	Cham :Springer International Publishing :2019.
Description:	xiv, 119 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Ergodic theory.
Online resource:	https://doi.org/10.1007/978-3-030-27390-3
ISBN:	9783030273903$q(electronic bk.)

An introduction to the Kolmogorov-Bernoulli equivalence
Ponce, Gabriel.

An introduction to the Kolmogorov-Bernoulli equivalence[electronic resource] /by Gabriel Ponce, Regis Varao. - Cham :Springer International Publishing :2019. - xiv, 119 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

Introduction -- Preliminaries in Ergodic Theory -- Kolmogorov-Bernoulli Equivalence for Ergodic Automorphism of T² -- Hyperbolic Structures and the Kolmogorov-Bernoulli Equivalence -- State of the Art -- Index.

This book offers an introduction to a classical problem in ergodic theory and smooth dynamics, namely, the Kolmogorov-Bernoulli (non)equivalence problem, and presents recent results in this field. Starting with a crash course on ergodic theory, it uses the class of ergodic automorphisms of the two tori as a toy model to explain the main ideas and technicalities arising in the aforementioned problem. The level of generality then increases step by step, extending the results to the class of uniformly hyperbolic diffeomorphisms, and concludes with a survey of more recent results in the area concerning, for example, the class of partially hyperbolic diffeomorphisms. It is hoped that with this type of presentation, nonspecialists and young researchers in dynamical systems may be encouraged to pursue problems in this area.

ISBN: 9783030273903$q(electronic bk.)

Standard No.: 10.1007/978-3-030-27390-3doiSubjects--Topical Terms:

219112
Ergodic theory.

LC Class. No.: QA313 / .P663 2019

Dewey Class. No.: 515.42

An introduction to the Kolmogorov-Bernoulli equivalence
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300 $a xiv, 119 p. : $b ill., digital ; $c 24 cm.
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505 0 $a Introduction -- Preliminaries in Ergodic Theory -- Kolmogorov-Bernoulli Equivalence for Ergodic Automorphism of T² -- Hyperbolic Structures and the Kolmogorov-Bernoulli Equivalence -- State of the Art -- Index.
520 $a This book offers an introduction to a classical problem in ergodic theory and smooth dynamics, namely, the Kolmogorov-Bernoulli (non)equivalence problem, and presents recent results in this field. Starting with a crash course on ergodic theory, it uses the class of ergodic automorphisms of the two tori as a toy model to explain the main ideas and technicalities arising in the aforementioned problem. The level of generality then increases step by step, extending the results to the class of uniformly hyperbolic diffeomorphisms, and concludes with a survey of more recent results in the area concerning, for example, the class of partially hyperbolic diffeomorphisms. It is hoped that with this type of presentation, nonspecialists and young researchers in dynamical systems may be encouraged to pursue problems in this area.
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