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.
This work is supported by the Russian Foundation for Basic Research (project nos. 15-01-03689‑a and 16-51-10005-Ko_a) and by the Russian Science Foundation (project no. 14-41-00044). The research is carried out within the HSE Basic Research Program (project no. 90) in 2017.
Citation:
V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev, “On the structure of the ambient manifold for Morse–Smale systems without heteroclinic intersections”, Order and chaos in dynamical systems, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov, Trudy Mat. Inst. Steklova, 297, MAIK Nauka/Interperiodica, Moscow, 2017, 201–210; Proc. Steklov Inst. Math., 297 (2017), 179–187
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\paper On the structure of the ambient manifold for Morse--Smale systems without heteroclinic intersections
\inbook Order and chaos in dynamical systems
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov
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\vol 297
\pages 201--210
\publ MAIK Nauka/Interperiodica
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