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Zap. Nauchn. Sem. POMI, 2015, Volume 432, Pages 128–161 (Mi znsl6115)  

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

Scaling entropy sequence: invariance and examples

P. B. Zatitskiyab

a Chebyshev Laboratory, St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

Abstract: A scaling entropy sequence of an automorphism is an entropy-type metric invariant suggested by A. M. Vershik. We confirm his conjecture that it does not depend on the choice of a semimetric. This means that it is indeed a metric invariant. We also calculate this invariant for several classical dynamical systems.

Key words and phrases: Lebesgue space, semimetric.

Full text: PDF file (328 kB)
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English version:
Journal of Mathematical Sciences (New York), 2015, 209:6, 890–909

UDC: 517.518.115+517.987.1+515.124.4
Received: 27.10.2014

Citation: P. B. Zatitskiy, “Scaling entropy sequence: invariance and examples”, Representation theory, dynamical systems, combinatorial methods. Part XXIV, Zap. Nauchn. Sem. POMI, 432, POMI, St. Petersburg, 2015, 128–161; J. Math. Sci. (N. Y.), 209:6 (2015), 890–909

Citation in format AMSBIB
\Bibitem{Zat15}
\by P.~B.~Zatitskiy
\paper Scaling entropy sequence: invariance and examples
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIV
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 432
\pages 128--161
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6115}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 209
\issue 6
\pages 890--909
\crossref{https://doi.org/10.1007/s10958-015-2536-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84939430961}


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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. P. B. Zatitskiy, “On the possible growth rate of a scaling entropy sequence”, J. Math. Sci. (N. Y.), 215:6 (2016), 715–733  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. A. M. Vershik, P. B. Zatitskii, “Universal adic approximation, invariant measures and scaled entropy”, Izv. Math., 81:4 (2017), 734–770  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Записки научных семинаров ПОМИ
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