Peixoto graph of Morse-Smale diffeomorphisms on manifolds of dimension greater than three

Abstract

Let Mn be a closed orientable manifold of dimension greater than three and G1(Mn) be the class of orientation-preserving Morse-Smale diffeomorphisms on Mn such that the set of unstable separatrices of every f ∈ G1(Mn) is one-dimensional and does not contain heteroclinic orbits. We show that the Peixoto graph is a complete invariant of topological conjugacy in G1(Mn).