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On Some Modifications of Arnold’s Cat Map

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Abstract

An effective method is proposed for constructing specific examples of Anosov diffeomorphisms on the torus \({{\mathbb{T}}^{2}},\) that are different from linear hyperbolic automorphisms. We introduce a special class of diffeomorphisms that are compositions of the well-known linear Arnold’s cat map and some diffeomorphisms homotopic to the identity. Constructively verified sufficient hyperbolicity conditions are established for this class of mappings.

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Funding

This work was funded by the Russian Science Foundation, grant no. 21-71-30011.

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Authors and Affiliations

  1. Center of Integrable Systems, Demidov Yaroslavl State University, Yaroslavl, Russia

    S. D. Glyzin & A. Yu. Kolesov

Authors
  1. S. D. Glyzin
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  2. A. Yu. Kolesov
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Correspondence to S. D. Glyzin or A. Yu. Kolesov.

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The authors declare that they have no conflicts of interest.

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Translated by I. Ruzanova

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Glyzin, S.D., Kolesov, A.Y. On Some Modifications of Arnold’s Cat Map. Dokl. Math. 104, 242–246 (2021). https://doi.org/10.1134/S1064562421050069

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  • DOI: https://doi.org/10.1134/S1064562421050069

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