Abstract:
J. Palis found necessary conditions for a Morse–Smale diffeomorphism on a closed n-dimensional manifold Mn to embed into a topological flow and proved that these conditions are also sufficient for n=2. For the case n=3 a possibility of wild embedding of closures of separatrices of saddles is an additional obstacle for Morse–Smale cascades to embed into topological flows. In this paper we show that there are no such obstructions for Morse–Smale diffeomorphisms without heteroclinic intersection given on the sphere Sn, n≥4, and Palis conditions again are sufficient for such diffeomorphisms.
Key words and phrases:
Morse–Smale dynamical systems, embedding in topological flows, topological classification.
Research is done with financial support of Russian Science Foundation (project 17-11-01041) except Section 4.3, which is done in the framework of the Basic Research Program of HSE in 2019.
Citation:
V. Grines, E. Gurevich, O. Pochinka, “On embedding of multidimensional Morse–Smale diffeomorphisms into topological flows”, Mosc. Math. J., 19:4 (2019), 739–760
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\paper On embedding of multidimensional Morse--Smale diffeomorphisms into topological flows
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\issue 4
\pages 739--760
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Linking options:
https://www.mathnet.ru/eng/mmj751
https://www.mathnet.ru/eng/mmj/v19/i4/p739
This publication is cited in the following 5 articles:
Timur V. Medvedev, Elena V. Nozdrinova, Olga V. Pochinka, “Components of Stable Isotopy Connectedness
of Morse – Smale Diffeomorphisms”, Regul. Chaotic Dyn., 27:1 (2022), 77–97
V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka, “On Embedding of the Morse–Smale Diffeomorphisms in a Topological Flow”, J Math Sci, 265:6 (2022), 868
V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, “On Realization of Topological Conjugacy Classes of Morse–Smale Cascades on the Sphere $S^n$”, Proc. Steklov Inst. Math., 310 (2020), 108–123
V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka, “O vklyuchenii diffeomorfizmov Morsa—Smeila v topologicheskii potok”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 66, no. 2, Rossiiskii universitet druzhby narodov, M., 2020, 160–181
V Grines, E Gurevich, O Pochinka, D Malyshev, “On topological classification of Morse–Smale diffeomorphisms on the sphere S n
(n > 3)”, Nonlinearity, 33:12 (2020), 7088
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