Classification of Morse-Smale diffeomorphisms with one-dimensional set of unstable separatrices

Abstract

Let Mn be a closed orientable manifold of dimension n > 3. We study the class G1(Mn) of orientation-preserving Morse-Smale diffeomorphisms of Mn such that the set of unstable separatrices of any f ∈ G1(Mn) is one-dimensional and does not contain heteroclinic intersections. We prove that the Peixoto graph (equipped with an automorphism) is a complete topological invariant for diffeomorphisms of class G1(Mn), and construct a standard representative for any class of topologically conjugate diffeomorphisms.