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

V. Z. Grines ; E. V. Zhuzhoma ; V. S. Medvedev

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Order and chaos in dynamical systems, Tome 297 (2017), pp. 201-210.

Résumé

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.

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