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

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

Published electronically:
April 9, 2001

MathSciNet review:
1828611

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

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