On the topology of the set of completely unstable flows

Author:
Zbigniew Nitecki

Journal:
Trans. Amer. Math. Soc. **252** (1979), 147-162

MSC:
Primary 58F10; Secondary 34D10

MathSciNet review:
534115

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Abstract: We show that: (1) on any open manifold other than the line or plane, there exist nonsingular flows with which can be perturbed, in the strong topology (any *r*), to flows with , and that (2) on certain open 3-manifolds there exist flows with which cannot be approximated, in the strong topology, by flows satisfying both and no -explosions. These examples give partial negative answers to the conjecture of Takens and White, that the completely unstable flows with the strong topology equal the closure of their interior.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1979-0534115-8

Keywords:
Completely unstable flow,
-explosion,
plug,
strong topology

Article copyright:
© Copyright 1979
American Mathematical Society