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Matematicheskie Trudy, 2017, Volume 20, Number 2, Pages 90–119
DOI: https://doi.org/10.17377/mattrudy.2017.20.205 (Mi mt325) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Estimates for correlation in dynamical systems: from Hölder continuous functions to general observables

I. V. Podviginab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (332 kB) Citations (2)
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DOI: https://doi.org/10.17377/mattrudy.2017.20.205
Abstract: For many dynamical systems that are popular in applications, estimates are known for the decay of correlation in the case of Hölder continuous functions. In the present article, we suggest an approach that allows us to obtain estimates for correlation in dynamical systems in the case of arbitrary functions. This approach is based on approximation and estimates are obtained with the use of known estimates for Hölder continuous functions. We apply our approach to transitive Anosov diffeomorphisms and derive the central limit theorem for the characteristic functions of certain sets with boundary of zero measure.
Key words: correlation, the best approximation, approximation spaces, Anosov diffeomorphisms, central limit theorem.
Received: 30.01.2017
English version:
Siberian Advances in Mathematics, 2018, Volume 28, Issue 3, Pages 187–206
DOI: https://doi.org/10.3103/S1055134418030045
Bibliographic databases:
Document Type: Article
UDC: 517.987.5+517.518.2+519.214
Language: Russian
Citation: I. V. Podvigin, “Estimates for correlation in dynamical systems: from Hölder continuous functions to general observables”, Mat. Tr., 20:2 (2017), 90–119; Siberian Adv. Math., 28:3 (2018), 187–206
Citation in format AMSBIB
\Bibitem{Pod17}
\by I.~V.~Podvigin
\paper Estimates for correlation in dynamical systems: from H\"older continuous functions to general observables
\jour Mat. Tr.
\yr 2017
\vol 20
\issue 2
\pages 90--119
\mathnet{http://mi.mathnet.ru/mt325}
\crossref{https://doi.org/10.17377/mattrudy.2017.20.205}
\elib{https://elibrary.ru/item.asp?id=30558046}
\transl
\jour Siberian Adv. Math.
\yr 2018
\vol 28
\issue 3
\pages 187--206
\crossref{https://doi.org/10.3103/S1055134418030045}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052114693}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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    References:32
    First page:9
     
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