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Mat. Sb., 2009, Volume 200, Number 8, Pages 147–160 (Mi msb7523)  

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

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.

DOI: https://doi.org/10.4213/sm7523

Full text: PDF file (525 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:8, 1247–1259

Bibliographic databases:

UDC: 517.938.5
MSC: 37D20
Received: 20.01.2009 and 25.03.2009

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Siemaszko A., Wojtkowski M.P., “Counting Berg partitions”, Nonlinearity, 24:9 (2011), 2383–2403  crossref  mathscinet  zmath  adsnasa  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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