SpringerBriefs in Mathematics

An Introduction to the Kolmogorov–Bernoulli Equivalence

Authors: Ponce, Gabriel, Azevedo Varão Filho, José Régis

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  • 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
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eBook $44.99
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  • ISBN 978-3-030-27390-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-030-27389-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.



About the authors

Gabriel Ponce is an Associate Professor at the Institute of Mathematics, Statistics and Scientific Computing (IMECC) at University of Campinas. He holds a Bachelor's degree in Mathematics (2009) and a PhD in Dynamical Systems (2014), both from the University of São Paulo (USP), under the supervision of Ali Tahzibi. He was also a visiting PhD student at Penn State University, USA, where he worked with Federico Rodriguez Hertz, followed by a period of postdoctoral study at the University of Campinas (UNICAMP). His main field of research is Dynamical Systems and Ergodic Theory.

Régis Varão holds a Bachelor's degree in Mathematics from the University of Campinas (Unicamp) and received his Master's degree (2008) and PhD (2012) from IMPA, under the supervision of Marcelo Viana.  He also engaged in postdoctoral at the University of São Paulo (USP) to work with Prof. Ali Tahzibi and at the University of Chicago to work with Prof. Amie Wilkinson. In 2014 he joined the Institute of Mathematics, Statistics and Scientific Computing (IMECC) at University of Campinas as an Associate Professor. He received an honorary mention for the best PhD thesis in mathematics in Brazil (Gutierrez Prize). His main research area is Dynamical Systems and Ergodic Theory.


Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-030-27390-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-030-27389-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to the Kolmogorov–Bernoulli Equivalence
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive licence to Springer Nature Switzerland AG
eBook ISBN
978-3-030-27390-3
DOI
10.1007/978-3-030-27390-3
Softcover ISBN
978-3-030-27389-7
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XIV, 119
Number of Illustrations
5 b/w illustrations
Topics