Download eBook Free: https://ouo.io/yBEqe8 An Introduction to the Kolmogorov–Bernoulli Equivalence By: Gabriel Ponce; Régis Varão Publisher: Springer Print ISBN: 9783030273897, 303027389X eText ISBN: 9783030273903, 3030273903 Copyright year: 2019 Format: EPUB Available from $ 59.99 USD SKU 9783030273903 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.
