Transactions of the American Mathematical Society

Author(s): Kazumine Moriyasu; Kazuhiro Sakai; Naoya Sumi
Journal: Trans. Amer. Math. Soc. 353 (2001), 3391-3408.
MSC (2000): Primary 37C10, 37C15, 37C75, 37D20, 37D50; Secondary 37B99, 54H20
Posted: April 9, 2001
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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

interior of the set of all topologically stable

vector fields coincides with the set of all vector fields satisfying Axiom A and the strong transversality condition.

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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: 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
Posted: April 9, 2001
Copyright of article: Copyright 2001, American Mathematical Society

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