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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 500, Pages 26–30
DOI: https://doi.org/10.31857/S2686954321050064 (Mi danma199) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

On some modifications of Arnold's cat map

S. D. Glyzin, A. Yu. Kolesov

Centre of Integrable Systems, P.G. Demidov Yaroslavl State University, Yaroslavl, Russia
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DOI: https://doi.org/10.31857/S2686954321050064
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.
Funding agency Grant number
Russian Science Foundation 21-71-30011
This work was funded by the Russian Science Foundation, grant no. 21-71-30011.
Presented: V. V. Kozlov
Received: 24.07.2021
Revised: 24.07.2021
Accepted: 08.08.2021
English version:
Doklady Mathematics, 2021, Volume 104, Issue 2, Pages 242–246
DOI: https://doi.org/10.1134/S1064562421050069
Bibliographic databases:
Document Type: Article
UDC: 517.926
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, “On some modifications of Arnold's cat map”, Dokl. RAN. Math. Inf. Proc. Upr., 500 (2021), 26–30; Dokl. Math., 104:2 (2021), 242–246
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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