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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Vector fields with topological stability


Authors: Kazumine Moriyasu, Kazuhiro Sakai and Naoya Sumi
Journal: Trans. Amer. Math. Soc. 353 (2001), 3391-3408
MSC (2000): Primary 37C10, 37C15, 37C75, 37D20, 37D50; Secondary 37B99, 54H20
Published electronically: April 9, 2001
MathSciNet review: 1828611
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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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Additional Information

Kazumine Moriyasu
Affiliation: Department of Mathematics, Tokushima University, Tokushima 770-8502, Japan
Email: moriyasu@ias.tokushima-u.ac.jp

Kazuhiro Sakai
Affiliation: Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan
Address at time of publication: Department of Mathematics, Utsunomiya University, Mine-machi 321-8505, Japan
Email: kazsaka@cc.kanagawa-u.ac.jp, sakaik01@kanagawa-u.ac.jp

Naoya Sumi
Affiliation: Department of Mathematics, Tokyo Metropolitan University, Tokyo 192-0397, Japan
Email: sumi@comp.metro-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02748-9
PII: S 0002-9947(01)02748-9
Keywords: Topologically stable, structurally stable, Axiom A, strong transversality condition, vector fields, flows
Received by editor(s): October 12, 1999
Received by editor(s) in revised form: June 28, 2000
Published electronically: April 9, 2001
Article copyright: © Copyright 2001 American Mathematical Society