On Realization of Topological Conjugacy Classes of Morse–Smale Cascades on the Sphere $S^n$

We consider the class $G(S^n)$ of orientation-preserving Morse–Smale diffeomorphisms defined on the sphere $S^n$ of dimension $n\geq 4$ under the assumption that the invariant manifolds of different saddle periodic points are disjoint. For diffeomorphisms in this class, we describe an algorithm for constructing representatives of all topological conjugacy classes.