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This article is cited in 17 scientific papers (total in 17 papers)
On embedding a Morse-Smale diffeomorphism on a 3-manifold in a topological flow
V. Z. Grinesa, E. Ya. Gurevicha, V. S. Medvedevb, O. V. Pochinkaa a N. I. Lobachevski State University of Nizhni Novgorod
b Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod
Abstract:
In this paper, for the case of 3-dimensional manifolds, we solve the Palis problem on finding necessary and sufficient conditions for a Morse-Smale cascade to embed in a topological flow. The set of such cascades is open
in the space of all diffeomorphisms, while the set of arbitrary diffeomorphisms that embed in a smooth
flow is nowhere dense. Also, we consider a class of diffeomorphisms that embed in a topological flow and prove that a complete topological invariant for this class is similar to the Andronova-Maier scheme and the Peixoto graph.
Bibliography: 26 titles.
Keywords:
Morse-Smale diffeomorphism, Morse-Smale cascade, embedding in a flow, dynamical systems on manifolds.
Received: 15.12.2011 and 02.05.2012
Citation:
V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, O. V. Pochinka, “On embedding a Morse-Smale diffeomorphism on a 3-manifold in a topological flow”, Mat. Sb., 203:12 (2012), 81–104; Sb. Math., 203:12 (2012), 1761–1784
Linking options:
https://www.mathnet.ru/eng/sm8094https://doi.org/10.1070/SM2012v203n12ABEH004286 https://www.mathnet.ru/eng/sm/v203/i12/p81
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Abstract page: | 564 | Russian version PDF: | 237 | English version PDF: | 11 | References: | 70 | First page: | 19 |
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