An Introduction to the Kolmogorov-Bernoulli Equivalence

• Κύριοι συγγραφείς: Ponce, Gabriel (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Varão, Régis (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Έκδοση: 1st ed. 2019.
• Σειρά: SpringerBriefs in Mathematics,
• Θέματα: Dynamics.; Ergodic theory.; Measure theory.; Functional analysis.; Dynamical Systems and Ergodic Theory.; Measure and Integration.; Functional Analysis.

 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. 

 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.