On the structure of the ambient manifold for Morse–Smale systems without heteroclinic intersections

It is shown that if a closed smooth orientable manifold $M^n$, $n\geq3$, admits a Morse–Smale system without heteroclinic intersections (the absence of periodic trajectories is additionally required in the case of a Morse–Smale flow), then this manifold is homeomorphic to the connected sum of manifolds whose structure is interconnected with the type and number of points that belong to the non-wandering set of the Morse–Smale system.