On Embedding of Separatrices of Morse – Smale Diffeomorphism on Manifolds of Dimension $n\geqslant 4$

We show that, for Morse – Smale diffemorphism $f\colon M^n\to M^n$, $n\geqslant 4$, the closure of one- and $(n-1)$-dimensional separatrices in a basin of a sink point $\omega$ forms a trivial frame that contrasts with the case $n=3$. This result is a first step in the solution of problems of topological classification, embedding in a flow and existence of energy functions for such diffeomorphisms.