On the existence of periodic orbits for continuous Morse-Smale flows

We consider the class of continuous Morse-Smale flows defined on a topological closed manifold $M^n$ of dimension $n$ which is not less than three, and such that the stable and unstable manifolds of saddle equilibrium states do not have intersection. We establish a relationship between the existence of such flows and topology of closed trajectories and topology of ambient manifold. Namely, it is proved that if $f^t$ (that is a continuous Morse-Smale flow from considered class) has $\mu$ sink and source equilibrium states and $\nu$ saddles of codimension one, and the fundamental group $\pi_1 (M ^ n)$ does not contain a subgroup isomorphic to the free product $g =\frac {1} {2} \left (\nu - \mu +2\right)$ copies of the group of integers $\mathbb {Z} $, then the flow $ f^t$ has at least one periodic trajectory.