The topological classification of diffeomorphisms of the two-dimensional torus with an orientable attractor
This paper is devoted to the topological classification of structurally stable diffeomorphisms of the two-dimensional torus whose non-wandering set consists of an orientable one-dimensional attractor and finitely many of 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 non-intersecting arcs. The classification of one-dimensional basis sets on surfaces is 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.