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

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 $n\ge4$, we construct a complete conjugacy invariant in the class of diffeomorphisms with a single saddle of codimension one.