Geodesic
On the structure of the ambient manifold for Morse--Smale systems without heteroclinic intersections
Informatics and Automation, Order and chaos in dynamical systems, Tome 297 (2017), pp. 201-210

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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. 
@article{TRSPY_2017_297_a9,
     author = {V. Z. Grines and E. V. Zhuzhoma and V. S. Medvedev},
     title = {On the structure of the ambient manifold for {Morse--Smale} systems without heteroclinic intersections},
     journal = {Informatics and Automation},
     pages = {201--210},
     publisher = {mathdoc},
     volume = {297},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_297_a9/}
}
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V. Z. Grines; E. V. Zhuzhoma; V. S. Medvedev. On the structure of the ambient manifold for Morse--Smale systems without heteroclinic intersections. Informatics and Automation, Order and chaos in dynamical systems, Tome 297 (2017), pp. 201-210. http://geodesic.mathdoc.fr/item/TRSPY_2017_297_a9/