Titlebook: An Introduction to the Kolmogorov–Bernoulli Equivalence; Gabriel Ponce,Régis Var?o Book 2019 The Author(s), under exclusive licence to Spr

Neonatal

An Introduction to the Kolmogorov–Bernoulli Equivalence

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Michael Jaekel,Karsten Bronnertexistence of invariant measures for a continuous map. In Sect. 2.2 we state the Birkhoff ergodic theorem and recall the definitions of ergodicity and mixing, two of the properties commonly cited in the ergodic hierarchy. In Sect. 2.3 we fix several notations for the operations among partitions, such

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dithiolethione

Book 2019lem, 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

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媒介

,Hyperbolic Structures and the Kolmogorov–Bernoulli Equivalence,hism (Theorem 4.1). Linear ergodic automorphisms of . are very particular examples of Anosov diffeomorphisms. In light of this fact we will show how to obtain the Kolmogorov property for .. Anosov diffeomorphisms (Theorem 4.8) and how we can use it to obtain the Bernoulli property (Theorem 4.9) in parallel to the argument used in Chap. ..

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incredulity

State of the Art,ies that appear along the arguments. The class derived from Anosov diffeomorphisms is the one for which the results differ the most from the results for Anosov diffeomorphisms, therefore we go deeper in this particular case and prove the key results which allow us to overcome the absence of complete hyperbolicity along the center direction.