Geometric Continued Fractions as Invariants in the Topological Classification of Anosov Diffeomorphisms of Tori

2009/02/04 by Grisha Kolutsky, Kolutsky, Grisha
Computer Science · Mathematics · #11H06 #11J70 (Primary) 37D20 #15A36 (Secondary) #37C15 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.DS #math.NT #msc:11H06 #msc:11J70 #msc:15A36 #msc:37C15 #msc:37D20 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0902.0661

12 pages. arXiv admin note: text overlap with arXiv:0711.0830

openalex publication_date 2009/02/04 · arxiv created 2009/06/22 · arxiv updated 2012/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show how an object from the combinatorially geometric version of the analytical number theory, namely geometric continued fractions, appears in the classical smooth dynamics, namely in the problem on the topological classification of Anosov diffeomorphisms of tori.

Citations

• On the hyperbolic automorphisms of the 2-torus and their Markov partitions
• Multidimensional Gauss Reduction Theory for conjugacy classes of SL(n,Z)

Related

• Pseudo-Anosovs from the perspective of their mapping tori
• Serendipitous decompositions of higher-dimensional continued fractions
• Chaotic and Topological Properties of Continued Fractions
• Notes on regularity of Anosov splitting
• Geometric structures in Topology, Geometry, Global Analysis and Dynamics