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Proceedings of the Steklov Institute of Mathematics

, Volume 270, Issue 1, pp 132–140 | Cite as

Gradient flows with wildly embedded closures of separatrices

  • E. V. ZhuzhomaEmail author
  • V. S. Medvedev
Article

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.

Keywords

Equilibrium Point STEKLOV Institute Invariant Manifold Stable Manifold Tubular Neighborhood 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Nizhni Novgorod State Pedagogical UniversityNizhni NovgorodRussia
  2. 2.Research Institute for Applied Mathematics and CyberneticsLobachevsky State University of Nizhni NovgorodNizhni NovgorodRussia

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