On the topological classification of Morse-Smale diffeomorphisms on the sphere $S^n$ via colored graphs

We consider a class $G$ of orientation-preserving Morse-Smale diffeomorphisms without heteroclinic intersections defined on the sphere $S^{n}$ of dimension $n>3$. For every diffeomorphism $f\in G$ corresponding colored graph $\Gamma_f$, endowed by a automorphism $P_f$, is found. We also give definition of isomorphism of such graphs. The result is stated that existing isomorphism of graphs $\Gamma_f, \Gamma_{f'}$ is the neccesary and sufficient condition of topological conjugacy of diffeomorphisms $f, f'\in G$, and thatan algorithm exists which recognizes this existence by linear time.