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Препринт

On the hyperbolic automorphisms of the 2-torus and their Markov partitions

A.V. Klimenko, Anosov D., Kolutsky G.
In the paper we give an introduction to Anosov diffeomorphisms, ways to represent their chaotic properties and some historical remarks on this subject. A complete classification of hyperbolic linear automorphisms of 2-torus is presented. We introduce a notion of pre-Markov partition for such automorphisms and give their classification and an algorithm for their construction.