Structural stability of C1 diffeomorphisms

Clark Robinson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

124 Scopus citations

Abstract

In this paper we prove that if f is a C1 diffeomorphism that satisfies Axiom A and the strong transversality condition then it is structurally stable. J. Robbin proved this theorem for C2 diffeomorphisms. In addition to reducing the amount of differentiability necessary to prove the theorem, we also give a new proof combining the df metric of Robbin with the stable and unstable manifold proof of D. Anosov. We also prove structural stability in the neighborhood of a single hyperbolic basic set (independent of its being part of a diffeomorphism that satisfies Axiom A and the strong transversality condition). These proofs are adapted to prove the structural stability of C1 flows in another paper.

Original languageEnglish (US)
Pages (from-to)28-73
Number of pages46
JournalJournal of Differential Equations
Volume22
Issue number1
DOIs
StatePublished - Sep 1976

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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