On topological classification of Morse–Smale diffeomorphisms on the sphere Sn (n > 3).

We consider the class G(Sn) of orientation preserving Morse–Smale diffeomorphisms of the sphere Sn of dimension n > 3, assuming that invariant manifolds of different saddle periodic points have no intersection. For any diffeomorphism f ∈ G(Sn), we define a coloured graph Γf that describes a mutual arrangement of invariant manifolds of saddle periodic points of the diffeomorphism f. We enrich the graph Γf by an automorphism Pf induced by dynamics of f and define the isomorphism notion between two coloured graphs. The aim of the paper is to show that two diffeomorphisms f, f′ ∈ G(Sn) are topologically conjugated if and only if the graphs Γf, Γf′ are isomorphic. Moreover, we establish the existence of a linear-time algorithm to distinguish coloured graphs of diffeomorphisms from the class G(Sn). [ABSTRACT FROM AUTHOR]