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Funktsional'nyi Analiz i ego Prilozheniya, 2011, Volume 45, Issue 1, Pages 69–78
DOI: https://doi.org/10.4213/faa3028 (Mi faa3028) 		 
This article is cited in 6 scientific papers (total in 6 papers)

A Special Ergodic Theorem for Anosov Diffeomorphisms on the 2-Torus

P. S. Saltykov

Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (204 kB) Citations (6)
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DOI: https://doi.org/10.4213/faa3028
Abstract: A strengthened version of the Birkhoff ergodic theorem for linear Anosov diffeomorphisms on the 2-torus is presented. Namely, it is proved that the Hausdorff dimension of the set of points at which partial limits of the time average strongly (by a constant) differ from the space average is strictly less than the dimension of the space (i.e., than 2).
Keywords: Hausdorff dimension, special ergodic theorem, Anosov diffeomorphism, Markov chain, large deviation theorem.
Received: 09.11.2009
English version:
Functional Analysis and Its Applications, 2011, Volume 45, Issue 1, Pages 56–63
DOI: https://doi.org/10.1007/s10688-011-0006-9
Bibliographic databases:
Document Type: Article
UDC: 517.987.5
Language: Russian
Citation: P. S. Saltykov, “A Special Ergodic Theorem for Anosov Diffeomorphisms on the 2-Torus”, Funktsional. Anal. i Prilozhen., 45:1 (2011), 69–78; Funct. Anal. Appl., 45:1 (2011), 56–63
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
     
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