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100   $a20191025d2019      u|         0
101 0 $aeng
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181   $ctxt$2rdacontent
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200 13$aAn Introduction to the Kolmogorov?Bernoulli Equivalence /$fby Gabriel Ponce, Régis Varão
205   $a1st ed. 2019.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019.
215   $a1 online resource (131 pages)
225 1 $aSpringerBriefs in Mathematics,$x2191-8198
311   $a3-030-27389-X 
327   $aIntroduction -- Preliminaries in Ergodic Theory -- Kolmogorov?Bernoulli Equivalence for Ergodic Automorphism of T² -- Hyperbolic Structures and the Kolmogorov?Bernoulli Equivalence -- State of the Art -- Index.
330   $aThis book offers an introduction to a classical problem in ergodic theory and smooth dynamics, namely, the Kolmogorov?Bernoulli (non)equivalence problem, and presents recent results in this field. Starting with a crash course on ergodic theory, it uses the class of ergodic automorphisms of the two tori as a toy model to explain the main ideas and technicalities arising in the aforementioned problem. The level of generality then increases step by step, extending the results to the class of uniformly hyperbolic diffeomorphisms, and concludes with a survey of more recent results in the area concerning, for example, the class of partially hyperbolic diffeomorphisms. It is hoped that with this type of presentation, nonspecialists and young researchers in dynamical systems may be encouraged to pursue problems in this area.
410  0$aSpringerBriefs in Mathematics,$x2191-8198
606   $aDynamics
606   $aErgodic theory
606   $aMeasure theory
606   $aFunctional analysis
606   $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
606   $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
615  0$aDynamics.
615  0$aErgodic theory.
615  0$aMeasure theory.
615  0$aFunctional analysis.
615 14$aDynamical Systems and Ergodic Theory.
615 24$aMeasure and Integration.
615 24$aFunctional Analysis.
676   $a515.42
676   $a515.42
700   $aPonce$b Gabriel$4aut$4http://id.loc.gov/vocabulary/relators/aut$0780985
702   $aVarão$b Régis$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
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906   $aBOOK
912   $a9910349317203321
996   $aAn Introduction to the Kolmogorov?Bernoulli Equivalence$92529862
997   $aUNINA