Geodesic
On some modifications of Arnold's cat map
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 26-30

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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. 
@article{DANMA_2021_500_a4,
     author = {S. D. Glyzin and A. Yu. Kolesov},
     title = {On some modifications of {Arnold's} cat map},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {26--30},
     publisher = {mathdoc},
     volume = {500},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_500_a4/}
}
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S. D. Glyzin; A. Yu. Kolesov. On some modifications of Arnold's cat map. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 26-30. http://geodesic.mathdoc.fr/item/DANMA_2021_500_a4/