On Morse--Smale Diffeomorphisms with Four Periodic Points on Closed Orientable Manifolds

Abstract

We study Morse--Smale diffeomorphisms of n-manifolds with four periodic points which are the only periodic points. We prove that for n= 3 these diffeomorphisms are gradient-like and define a class of diffeomorphisms inevitably possessing a nonclosed heteroclinic curve. For n ≥ 4, we construct a complete conjugacy invariant in the class of diffeomorphisms with a single saddle of codimension one.