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An Introduction to the Kolmogorov-Bernoulli Equivalence / by Gabriel Ponce, Régis Varão.

Author/Creator:
Ponce, Gabriel. author., Author,
Publication:
Cham : Springer International Publishing : Imprint: Springer, 2019.
Format/Description:
Book
1 online resource (XIV, 119 pages) : 5 illustrations
Edition:
1st ed. 2019.
Series:
Mathematics and Statistics (Springer-11649)
SpringerBriefs in mathematics 2191-8198
SpringerBriefs in Mathematics, 2191-8198
Contained In:
Springer eBooks
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Details

Subjects:
Dynamics.
Ergodic theory.
Measure theory.
Functional analysis.
Local subjects:
Dynamical Systems and Ergodic Theory. (search)
Measure and Integration. (search)
Functional Analysis. (search)
System Details:
text file PDF
Summary:
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.
Contents:
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.
Contributor:
Varão, Régis. author., Author,
SpringerLink (Online service)
Other format:
Printed edition:
Printed edition:
ISBN:
978-3-030-27390-3
9783030273903
Publisher Number:
10.1007/978-3-030-27390-3 doi
Access Restriction:
Restricted for use by site license.