On Some Modifications of Arnold’s Cat Map

S. D. Glyzin^a^,* and A. Yu. Kolesov^a^,**

^aCenter of Integrable Systems, Demidov Yaroslavl State University, Yaroslavl, Russia

Correspondence to: *e-mail: glyzin.s@gmail.com
Correspondence to: **e-mail: andkolesov@mail.ru

Received 24 July, 2021

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.

Keywords: Arnold’s cat map, hyperbolicity, torus, Anosov diffeomorphism

DOI: 10.1134/S1064562421050069