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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 436, Pages 101–111 (Mi znsl6161)  
This article is cited in 4 scientific papers (total in 4 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
Full-text PDF (181 kB) Citations (4)
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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 G. Sinai and the definition from the unpublished master thesis by D. Z. Arov (1957).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.
Received: 22.09.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 215, Issue 6, Pages 693–699
DOI: https://doi.org/10.1007/s10958-016-2874-2
Bibliographic databases:
Document Type: Article
UDC: 517.987.5+517.838
Language: Russian
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://mathscinet.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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84966549769}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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