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Structural stability of vector fields with shadowing

Authors
Journal
Journal of Differential Equations
0022-0396
Publisher
Elsevier
Publication Date
Volume
232
Issue
1
Identifiers
DOI: 10.1016/j.jde.2006.08.012
Keywords
  • Vector Field
  • Shadowing
  • Structurally Stable
  • Axiom A
  • Strong Transversality Condition

Abstract

Abstract Let X be a C 1 vector field without singularities. In this paper, we show that X is in the C 1 interior of the set of vector fields with the shadowing property if and only if X satisfies both Axiom A and the strong transversality condition; that is, X is structurally stable.

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