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Sufficient condition for the hyperbolicity of mappings of the torus

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Abstract

We consider mappings of the m-dimensional torus Tm (m ≥ 2) that are C 1-perturbations of linear hyperbolic automorphisms. We obtain sufficient conditions for such mappings to be one-to-one hyperbolic mappings (i.e., Anosov diffeomorphisms). These results are used to study the blue-sky catastrophe related to the vanishing of a saddle-node invariant torus with a quasiperiodic winding in a system of ordinary differential equations.

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Authors and Affiliations

  1. Demidov Yaroslavl State University, Yaroslavl, 150000, Russia

    A. Yu. Kolesov

  2. Lomonosov Moscow State University, Moscow, 119992, Russia

    N. Kh. Rozov & V. A. Sadovnichii

Authors
  1. A. Yu. Kolesov
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  2. N. Kh. Rozov
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  3. V. A. Sadovnichii
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Correspondence to A. Yu. Kolesov.

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Original Russian Text © A.Yu. Kolesov, N.Kh. Rozov, V.A. Sadovnichii, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 4, pp. 465–486.

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Kolesov, A.Y., Rozov, N.K. & Sadovnichii, V.A. Sufficient condition for the hyperbolicity of mappings of the torus. Diff Equat 53, 457–478 (2017). https://doi.org/10.1134/S001226611704005X

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  • DOI: https://doi.org/10.1134/S001226611704005X

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