An Introduction to the Kolmogorov–Bernoulli Equivalence / Gabriel Ponce, Régis Varão

By:

Ponce, Gabriel [VerfasserIn]

Contributor(s):

Varão, Régis [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerBriefs in Mathematics | SBMAC SpringerBriefs | Springer eBooks Mathematics and StatisticsPublisher: Cham : Springer, [2019]Copyright date: © 2019Description: 1 Online-Ressource (XIV, 119 Seiten) : Illustrationen, DiagrammeISBN:

9783030273903

Subject(s):

Additional physical formats: 9783030273897 | Erscheint auch als: 978-3-030-27389-7 Druck-AusgabeLOC classification:

QA313

DOI: DOI: 10.1007/978-3-030-27390-3Online resources:

Summary: Introduction -- Preliminaries in Ergodic Theory -- Kolmogorov–Bernoulli Equivalence for Ergodic Automorphism of T² -- Hyperbolic Structures and the Kolmogorov–Bernoulli Equivalence -- State of the Art -- IndexSummary: 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 areaPPN: PPN: 1681722003Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS

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