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arXiv · 0810.5269

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

Dmitry V. Anosov·Alexey V. Klimenko·Grisha Kolutsky
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Abstract

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.

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Dmitry V. Anosov, Alexey V. Klimenko, Grisha Kolutsky. 2008-10-29. On the hyperbolic automorphisms of the 2-torus and their Markov partitions. https://arxiv.org/abs/0810.5269

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