The Topological Classification of Diffeomorphisms of the Two-Dimensional Torus with an Orientable Attractor
Received 30 November 2020; accepted 14 December 2020
2020, Vol. 16, no. 4, pp. 595-606
Author(s): Grines V. Z., Kruglov E. V., Pochinka O. V.
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.
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