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Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 3, Pages 22–31 (Mi faa3580)  

Affinity of the Arov Entropy

B. M. Gurevichab

a Lomonosov Moscow State University
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow

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.

Keywords: 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.

DOI: https://doi.org/10.4213/faa3580

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English version:
Functional Analysis and Its Applications, 2018, 52:3, 178–185

Bibliographic databases:

UDC: 519.24
Received: 08.04.2018

Citation: B. M. Gurevich, “Affinity of the Arov Entropy”, Funktsional. Anal. i Prilozhen., 52:3 (2018), 22–31; Funct. Anal. Appl., 52:3 (2018), 178–185

Citation in format AMSBIB
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