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 Rus. J. Nonlin. Dyn., 2020, Volume 16, Number 4, Pages 595–606 (Mi nd731)

Mathematical problems of nonlinearity

The Topological Classification of Diffeomorphisms of the Two-Dimensional Torus with an Orientable Attractor

V. Z. Grinesa, E. V. Kruglovb, O. V. Pochinkaa

a National Research University Higher School of Economics, ul. B. Pecherskaya 25/12, Nizhny Novgorod, 603150 Russia
b Lobachevsky State University of Nizhny Novgorod, prosp. Gagarina 23, Nizhny Novgorod, 603950 Russia

Abstract: This paper is devoted to the topological classification of structurally stable diffeomorphisms of the two-dimensional torus whose nonwandering set consists of an orientable one-dimensional attractor and finitely many isolated source and saddle periodic points, under the assumption that the closure of the union of the stable manifolds of isolated periodic points consists of simple pairwise nonintersecting arcs. The classification of one-dimensional basis sets on surfaces has been exhaustively obtained in papers by V. Grines. He also obtained a classification of some classes of structurally stable diffeomorphisms of surfaces using combined algebra-geometric invariants. In this paper, we distinguish a class of diffeomorphisms that admit purely algebraic differentiating invariants.

Keywords: A-diffeomorphisms of a torus, topological classification, orientable attractor

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 075-15-2019-1931 This work was performed with support of the Laboratory of Dynamical Systems and Applications NRU HSE of the Ministry of science and higher education of the RF grant no 075-15-2019-1931.

DOI: https://doi.org/10.20537/nd200405

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MSC: 37D20
Accepted:14.12.2020

Citation: V. Z. Grines, E. V. Kruglov, O. V. Pochinka, “The Topological Classification of Diffeomorphisms of the Two-Dimensional Torus with an Orientable Attractor”, Rus. J. Nonlin. Dyn., 16:4 (2020), 595–606

Citation in format AMSBIB
\Bibitem{GriKruPoc20} \by V. Z. Grines, E. V. Kruglov, O. V. Pochinka \paper The Topological Classification of Diffeomorphisms of the Two-Dimensional Torus with an Orientable Attractor \jour Rus. J. Nonlin. Dyn. \yr 2020 \vol 16 \issue 4 \pages 595--606 \mathnet{http://mi.mathnet.ru/nd731} \crossref{https://doi.org/10.20537/nd200405} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=4198782}