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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Vector fields with topological stability
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by Kazumine Moriyasu, Kazuhiro Sakai and Naoya Sumi PDF
Trans. Amer. Math. Soc. 353 (2001), 3391-3408 Request permission

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
  • MR Author ID: 610209
  • Email: sumi@comp.metro-u.ac.jp
  • Received by editor(s): October 12, 1999
  • Received by editor(s) in revised form: June 28, 2000
  • Published electronically: April 9, 2001
  • © Copyright 2001 American Mathematical Society
  • 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
  • MathSciNet review: 1828611