An Introduction to the Kolmogorov–Bernoulli Equivalence
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Beschreibung
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.
Offers a new, easier-to-grasp approach on the Kolmogorov–Bernoulli equivalence Uses a myriad of tools, like the Lyapunov exponent and Pesin’s theory, to present the KB equivalence in other frameworks Includes a survey of recent results in the field
Autor*in
Gabriel Ponce
Themen in »An Introduction to the Kolmogorov–Bernoulli Equivalence«
Kolmogorov systems Bernoulli systems ergodic theory isomorphism problem disintegration of measures 37A35 37C40 37D30
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“All the proofs given in the book are complete, the list of references is adequate and the language is very clear, making the reading captivating.” (Sergey Gennadievich Kryzhevich, Mathematical Reviews, May, 2021)
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