Geodesic
The number of classes of Markov partitions for a~hyperbolic automorphism of a~2-torus
Sbornik. Mathematics, Tome 200 (2009) no. 8, pp. 1247-1259

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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, continued fractions.
Mots-clés : Markov partitions 
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     title = {The number of classes of {Markov} partitions for a~hyperbolic automorphism of a~2-torus},
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A. V. Klimenko. The number of classes of Markov partitions for a~hyperbolic automorphism of a~2-torus. Sbornik. Mathematics, Tome 200 (2009) no. 8, pp. 1247-1259. http://geodesic.mathdoc.fr/item/SM_2009_200_8_a6/