An introduction to the Kolmogorov-Bernoulli equivalence
Author(s)
Bibliographic Information
An introduction to the Kolmogorov-Bernoulli equivalence
（SpringerBriefs in mathematics, . SBMAC SpringerBriefs）
Springer, c2019
Available at 4 libraries
Note
Includes bibliographical references and index
Description and Table of Contents
Description
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.
Table of Contents
Introduction.- Preliminaries in Ergodic Theory.- Kolmogorov-Bernoulli Equivalence for Ergodic Automorphism of T(2).- Hyperbolic Structures and the Kolmogorov-Bernoulli Equivalence.- State of the Art.- Index.
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