An introduction to the Kolmogorov-Bernoulli equivalence
著者
書誌事項
An introduction to the Kolmogorov-Bernoulli equivalence
（SpringerBriefs in mathematics, . SBMAC SpringerBriefs）
Springer, c2019
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
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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