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Sbornik: Mathematics, 2009, Volume 200, Issue 8, Pages 1247–1259
DOI: https://doi.org/10.1070/SM2009v200n08ABEH004036 (Mi sm7523) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The number of classes of Markov partitions for a hyperbolic automorphism of a 2-torus

A. V. Klimenko

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (300 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM2009v200n08ABEH004036
Abstract: The Markov partitions constructed by Adler and Weiss and the pre-Markov partitions related to them are important in the investigation of the properties of an Anosov diffeomorphism of a 2-torus. A connection is established between the number of equivalence classes of the simplest pre-Markov partitions of a fixed diffeomorphism with respect to the natural equivalence and the continued fraction expressing the slope of the unstable direction of the matrix defining this diffeomorphism.
Bibliography: 7 titles.
Keywords: Anosov diffeomorphisms, Markov partitions, continued fractions.
Received: 20.01.2009 and 25.03.2009
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 8, Pages 147–160
DOI: https://doi.org/10.4213/sm7523
Bibliographic databases:
UDC: 517.938.5
MSC: 37D20
Language: English
Original paper language: Russian
Citation: A. V. Klimenko, “The number of classes of Markov partitions for a hyperbolic automorphism of a 2-torus”, Mat. Sb., 200:8 (2009), 147–160; Sb. Math., 200:8 (2009), 1247–1259
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    Russian version PDF:228
    English version PDF:7
    References:48
    First page:11
     
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