An example of a local flow on a manifold

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Abstract

Let p be a point of a smooth n-dimensional manifold. If n is even it is easy to construct a local flow about p such that p is an isolated critical point and no orbit except the stationary one at/? has/as a limit point. We call such a flow a nonnull flow about p (NN flow). Mendelson has conjectured that NN flows do not exist on odd dimensional manifolds. We show that Mendelson's conjecture is false by constructing an NN-flow on any smooth manifold whose dimension is an odd integer exceeding one.

Original languageEnglish (US)
Pages (from-to)208-213
Number of pages6
JournalProceedings of the American Mathematical Society
Volume42
Issue number1
DOIs
StatePublished - Jan 1974

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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