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.
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.
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
\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://mathscinet.ams.org/mathscinet-getitem?mr=4198782}
Citation in format AMSBIB
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