Construction of diffeomorphisms with a finite number of orbits of heteroclinic tangencies on surfaces

In the present report we obtain complete topological classification of diffeomorphisms $f$ given on an orientable two-dimensional surfaces and satisfying the conditions below: 1) $\Omega(f)$ consists of a finite number of hyperbolic fixed points and saddle fixed points having negative index; 2) wandering set of $f$ contains a finite number of heteroclinic orbits of transversal and non-transversal intersections. We solve the realization problem, that is we construct a diffeomorphism in each class of topological conjugacy of diffeomorphisms from the set $\Psi$.