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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics