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

• Autore: Ponce Gabriel
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019
• Edizione: 1st ed. 2019.
• Descrizione fisica: 1 online resource (131 pages)
• Disciplina: 515.42
• Soggetto topico: Dynamics; Ergodic theory; Measure theory; Functional analysis; Dynamical Systems and Ergodic Theory; Measure and Integration; Functional Analysis
• Persona (resp. second.): VarãoRégis
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: An Introduction to the Kolmogorov–Bernoulli Equivalence
• ISBN: 3-030-27390-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910349317203321
• Lo trovi qui: Univ. Federico II
• Serie: SpringerBriefs in Mathematics, . 2191-8198