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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 270, Pages 138–146
(Mi tm3009)
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This article is cited in 2 scientific papers (total in 2 papers)
Gradient flows with wildly embedded closures of separatrices
E. V. Zhuzhomaa, V. S. Medvedevb a Nizhni Novgorod State Pedagogical University, Nizhni Novgorod, Russia
b Research Institute for Applied Mathematics and Cybernetics, Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia
Abstract:
We show that for any $n\ge4$ there exists an $n$-dimensional closed manifold $M^n$ on which one can define a Morse–Smale gradient flow $f^t$ with two nodes and two saddles such that the closure of the separatrix of some saddle of $f^t$ is a wildly embedded sphere of codimension 2. We also prove that the closures of separatrices of a flow with three equilibrium points are always embedded in a locally flat way.
Received in March 2009
Citation:
E. V. Zhuzhoma, V. S. Medvedev, “Gradient flows with wildly embedded closures of separatrices”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 270, MAIK Nauka/Interperiodica, Moscow, 2010, 138–146; Proc. Steklov Inst. Math., 270 (2010), 132–140
Linking options:
https://www.mathnet.ru/eng/tm3009 https://www.mathnet.ru/eng/tm/v270/p138
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Abstract page: | 283 | Full-text PDF : | 65 | References: | 87 |
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