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Zap. Nauchn. Sem. POMI, 2015, Volume 436, Pages 101–111 (Mi znsl6161)  

This article is cited in 3 scientific papers (total in 3 papers)

Toward the history of dynamical entropy: comparing two definitions

B. M. Gurevichab

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

Abstract: Two definitions are compared for the measure-theoretic entropy of an automorphism of a Lebesgue space: the commonly known definition suggested in 1959 by Ya. G. Sinai and the definition from the unpublished master thesis by D.Ż. Arov (1957). The result is that the two definitions lead to essentially the same object in the class of ergodic automorphisms, while for the nonergodic case the situation is in general different.

Key words and phrases: metric entropy, dinamical entropy, partition of a Lebesgue space, generating partition (generator), Bernoulli factor automorphism.

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English version:
Journal of Mathematical Sciences (New York), 2016, 215:6, 693–699

Bibliographic databases:

UDC: 517.987.5+517.838
Received: 22.09.2015

Citation: B. M. Gurevich, “Toward the history of dynamical entropy: comparing two definitions”, Representation theory, dynamical systems, combinatorial methods. Part XXV, Zap. Nauchn. Sem. POMI, 436, POMI, St. Petersburg, 2015, 101–111; J. Math. Sci. (N. Y.), 215:6 (2016), 693–699

Citation in format AMSBIB
\Bibitem{Gur15}
\by B.~M.~Gurevich
\paper Toward the history of dynamical entropy: comparing two definitions
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXV
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 436
\pages 101--111
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6161}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3498187}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 215
\issue 6
\pages 693--699
\crossref{https://doi.org/10.1007/s10958-016-2874-2}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84966549769}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. Z. Arov, “To the history of the appearance of the notion of $\epsilon$-entropy of an authomorphism of a Lebesque space and $(\varepsilon,T)$-entropy of a dynamical system with continuous time”, J. Math. Sci. (N. Y.), 215:6 (2016), 677–692  mathnet  crossref  mathscinet
    2. A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. B. M. Gurevich, “Affinity of the Arov Entropy”, Funct. Anal. Appl., 52:3 (2018), 178–185  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Записки научных семинаров ПОМИ
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