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

Abstract

It is shown that if a closed smooth orientable manifold Mⁿ, n ≥ 3, 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.