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

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

2008-10-29

arxiv.org/abs/0810.5269v1

Mathematics

Dynamical Systems

34 pages, 5 figures, published as a preprint of Max Planck Institute for Mathematics MPIM2008-54, see http://www.mpim-bonn.m

Scientific paper

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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