Vector fields with topological stability

Moriyasu, Kazumine; Sakai, Kazuhiro; Sumi, Naoya

doi:10.1090/S0002-9947-01-02748-9

Vector fields with topological stability
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by Kazumine Moriyasu, Kazuhiro Sakai and Naoya Sumi

Trans. Amer. Math. Soc. 353 (2001), 3391-3408

DOI: https://doi.org/10.1090/S0002-9947-01-02748-9

Published electronically: April 9, 2001

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Abstract:

In this paper, we give a characterization of the structurally stable vector fields by making use of the notion of topological stability. More precisely, it is proved that the $C^1$ interior of the set of all topologically stable $C^1$ vector fields coincides with the set of all vector fields satisfying Axiom A and the strong transversality condition.

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