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

Dmitry V. Anosov; Alexey V. Klimenko; Grisha Kolutsky

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

Dynamical Systems 2008-10-30 v1

Authors: Dmitry V. Anosov , Alexey V. Klimenko , Grisha Kolutsky

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.

Keywords

anosov diffeomorphism hyperbolic automorphism 2-torus markov partition pre-markov partition chaotic dynamics

Cite

@article{arxiv.0810.5269,
  title  = {On the hyperbolic automorphisms of the 2-torus and their Markov partitions},
  author = {Dmitry V. Anosov and Alexey V. Klimenko and Grisha Kolutsky},
  journal= {arXiv preprint arXiv:0810.5269},
  year   = {2008}
}

Comments

34 pages, 5 figures, published as a preprint of Max Planck Institute for Mathematics MPIM2008-54, see http://www.mpim-bonn.mpg.de/preprints/send?bid=3586

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

Abstract

Keywords

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