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Funktsional. Anal. i Prilozhen., 2014, Volume 48, Issue 4, Pages 70–74 (Mi faa3165)  

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

Brief communications

On a Scaling Entropy Sequence of a Dynamical System

P. B. Zatitskiiab

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

Abstract: We present a series of statements about scaling entropy, a metric invariant of dynamical systems proposed by A. M. Vershik in the late 1990s. We show that this is indeed a metric invariant and calculate it in several special cases.

Keywords: metric invariants, entropy, scaling sequence, $\varepsilon$-entropy

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0026
MK-6133.2013.1
Gazprom Neft
Saint Petersburg State University 6.38.223.2014
Russian Foundation for Basic Research 13-01-12422 офи_м2
14-01-00373_а


DOI: https://doi.org/10.4213/faa3165

Full text: PDF file (169 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2014, 48:4, 291–294

Bibliographic databases:

UDC: 517.987.5
Received: 01.09.2014

Citation: P. B. Zatitskii, “On a Scaling Entropy Sequence of a Dynamical System”, Funktsional. Anal. i Prilozhen., 48:4 (2014), 70–74; Funct. Anal. Appl., 48:4 (2014), 291–294

Citation in format AMSBIB
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  • https://doi.org/10.4213/faa3165
  • http://mi.mathnet.ru/eng/faa/v48/i4/p70

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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, “Scaling entropy sequence: invariance and examples”, J. Math. Sci. (N. Y.), 209:6 (2015), 890–909  mathnet  crossref
    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
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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