03214nam 22006135 450 991034931720332120200701140307.03-030-27390-310.1007/978-3-030-27390-3(CKB)4100000009678241(MiAaPQ)EBC5968955(DE-He213)978-3-030-27390-3(PPN)269149511(EXLCZ)99410000000967824120191025d2019 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierAn Introduction to the Kolmogorov–Bernoulli Equivalence /by Gabriel Ponce, Régis Varão1st ed. 2019.Cham :Springer International Publishing :Imprint: Springer,2019.1 online resource (131 pages)SpringerBriefs in Mathematics,2191-81983-030-27389-X 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.SpringerBriefs in Mathematics,2191-8198DynamicsErgodic theoryMeasure theoryFunctional analysisDynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XMeasure and Integrationhttps://scigraph.springernature.com/ontologies/product-market-codes/M12120Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Dynamics.Ergodic theory.Measure theory.Functional analysis.Dynamical Systems and Ergodic Theory.Measure and Integration.Functional Analysis.515.42515.42Ponce Gabrielauthttp://id.loc.gov/vocabulary/relators/aut780985Varão Régisauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910349317203321An Introduction to the Kolmogorov–Bernoulli Equivalence2529862UNINA