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

2008/10/29 by Dmitry V. Anosov, Anosov, Dmitry V., Alexey V. Klimenko +3 · 2 citations
Mathematics · #37D20 #37E30 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DS #msc:37D20 #msc:37E30

paper · pdf · doi:10.48550/arxiv.0810.5269

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

arxiv created 2008/10/29 · openalex publication_date 2008/10/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Cited by

• Geometric Continued Fractions as Invariants in the Topological Classification of Anosov Diffeomorphisms of Tori
• Counting Berg partitions

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