An example of a local flow on a manifold
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- by Denis L. Blackmore PDF
- Proc. Amer. Math. Soc. 42 (1974), 208-213 Request permission
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 p has p 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.References
- Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
- John W. Milnor, Topology from the differentiable viewpoint, University Press of Virginia, Charlottesville, Va., 1965. Based on notes by David W. Weaver. MR 0226651
- James R. Munkres, Elementary differential topology, Annals of Mathematics Studies, No. 54, Princeton University Press, Princeton, N.J., 1963. Lectures given at Massachusetts Institute of Technology, Fall, 1961. MR 0163320
- Shlomo Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0193578
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 208-213
- MSC: Primary 58F10; Secondary 34C40
- DOI: https://doi.org/10.1090/S0002-9939-1974-0326776-4
- MathSciNet review: 0326776