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＜E-Book＞
An Introduction to the Kolmogorov–Bernoulli Equivalence / by Gabriel Ponce, Régis Varão
(SpringerBriefs in Mathematics. ISSN:21918201)

Edition	1st ed. 2019.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2019
Size	XIV, 119 p. 5 illus : online resource
Authors	*Ponce, Gabriel author Varão, Régis author SpringerLink (Online service)
Subjects	LCSH:Dynamical systems LCSH:Measure theory LCSH:Functional analysis FREE:Dynamical Systems FREE:Measure and Integration FREE:Functional Analysis
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-030-27390-3

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