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Functional Analysis and Its Applications

, Volume 52, Issue 3, pp 178–185 | Cite as

Affinity of the Arov Entropy

  • B. M. GurevichEmail author
Article
  • 23 Downloads

Abstract

In this work we continue the study of historically the first version of dynamical entropy. This version was suggested in master’s thesis by D. Arov and went practically unnoticed. The main result of the paper is that the Arov entropy, like the Kolmogorov–Sinai entropy, has the affine property. This, in particular, allows constructing a variety of dynamical systems where the Arov entropy is not determined by the Kolmogorov–Sinai entropy.

Key words

Lebesgue space automorphism decomposition into ergodic components automorphism generator Bernoulli partition Kolmogorov–Sinai entropy automorphism entropy with respect to a partition mean entropy over the elements of a fixed partition 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Institute for Information Transmission Problems of Russian Academy of SciencesMoscowRussia

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