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Proceedings of the American Mathematical Society
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
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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 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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0326776-4
PII: S 0002-9939(1974)0326776-4
Article copyright: © Copyright 1974 American Mathematical Society