Realization of homotopy classes of torus homeomorphisms by the simplest structurally stable diffeomorphisms

Abstract. According to Thurston’s classification, the set of homotopy classes orientation-preserving homeomorphisms orientable surfaces is split into four disjoint subsets. A class from each subset characterized by existence a homeomorphism called canonical form, namely: periodic homeomorphism, reducible nonperiodic algebraically finite order, that not an and pseudo-Anosov homeomorphism. forms are structurally stable diffeomorphisms. Therefore, problem naturally arises constructing simplest (in certain sense) diffeomorphisms in class. In this paper, posed solved for torus homeomorphisms. class, representatives analytically constructed, namely, gradient-like diffeomorphism, Morse-Smale diffeomorphism with heteroclinic, Anosov which particular case diffeomorphism.