Sufficient conditions of topological conjugacy of diffeomorphisms with heteroclinic contacts on surfaces

In the present paper we consider diffeomorphisms that are given on the orientable two-dimensional surfaces and which nonwandering set consists of a finite number of hyperbolic fixed points and wandering set contains a finite number of heteroclinic orbits of transversal and non-transversal intersections. For some class of diffeomorphisms it is proved sufficient conditions of topological conjugacy.