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

Let $M^n$ be a closed orientable manifold of dimension $n>3$. We study the class $G_1(M^n)$ of orientation-preserving Morse–Smale diffeomorphisms of $M^n$ such that the set of unstable separatrices of any $f\in G_1(M^n)$ 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 $G_1(M^n)$, and construct a standard representative for any class of topologically conjugate diffeomorphisms.