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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.
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”, Sb. Math., 200:8 (2009), 1247–1259
Linking options:
https://www.mathnet.ru/eng/sm7523https://doi.org/10.1070/SM2009v200n08ABEH004036 https://www.mathnet.ru/eng/sm/v200/i8/p147
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