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

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.