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Gradient flows with wildly embedded closures of separatrices

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Abstract

We show that for any n ≥ 4 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.

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Authors and Affiliations

  1. Nizhni Novgorod State Pedagogical University, ul. Ul’yanova 1, Nizhni Novgorod, 603950, Russia

    E. V. Zhuzhoma

  2. Research Institute for Applied Mathematics and Cybernetics, Lobachevsky State University of Nizhni Novgorod, ul. Ul’yanova 10, Nizhni Novgorod, 603005, Russia

    V. S. Medvedev

Authors
  1. E. V. Zhuzhoma
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  2. V. S. Medvedev
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Correspondence to E. V. Zhuzhoma.

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Original Russian Text © E.V. Zhuzhoma, V.S. Medvedev, 2010, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Vol. 270, pp. 138–146.

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Zhuzhoma, E.V., Medvedev, V.S. Gradient flows with wildly embedded closures of separatrices. Proc. Steklov Inst. Math. 270, 132–140 (2010). https://doi.org/10.1134/S0081543810030090

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