An Introduction to the Kolmogorov–Bernoulli Equivalence

  • Gabriel Ponce
  • Régis Varão

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Gabriel Ponce, Régis Varão
    Pages 1-7
  3. Gabriel Ponce, Régis Varão
    Pages 9-32
  4. Gabriel Ponce, Régis Varão
    Pages 57-90
  5. Gabriel Ponce, Régis Varão
    Pages 91-116
  6. Back Matter
    Pages 117-119

About this book


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.


Kolmogorov systems Bernoulli systems ergodic theory isomorphism problem disintegration of measures 37A35 37C40 37D30

Authors and affiliations

  • Gabriel Ponce
    • 1
  • Régis Varão
    • 2
  1. 1.IMECCUniversity of Campinas - UNICAMPCampinasBrazil
  2. 2.IMECCUniversity of Campinas - UNICAMPCampinasBrazil

Bibliographic information

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