Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



An example of a local flow on a manifold

Author: Denis L. Blackmore
Journal: Proc. Amer. Math. Soc. 42 (1974), 208-213
MSC: Primary 58F10; Secondary 34C40
MathSciNet review: 0326776
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
  • [2] John W. Milnor, Topology from the differentiable viewpoint, Based on notes by David W. Weaver, The University Press of Virginia, Charlottesville, Va., 1965. MR 0226651
  • [3] James R. Munkres, Elementary differential topology, Lectures given at Massachusetts Institute of Technology, Fall, vol. 1961, Princeton University Press, Princeton, N.J., 1963. MR 0163320
  • [4] Shlomo Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0193578

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F10, 34C40

Retrieve articles in all journals with MSC: 58F10, 34C40

Additional Information

Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society