Stability theorems and hyperbolicity in dynamical systems

Clark Robinson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

122 Scopus citations

Abstract

We present an approach to proving structural stability and semi-stability theorems for diffeomorphisms and flows using the idea of shadowing an ∈-chain. We treat the cases when the whole manifold is hyperbolic and when the chain recurrent set is hyperbolic and the strong transversality condition is satisfied. The last two sections discuss the progress made on the converse to the structural stability theorem and a criterion for hyperbolicity.

Original languageEnglish (US)
Pages (from-to)425-437
Number of pages13
JournalRocky Mountain Journal of Mathematics
Volume7
Issue number3
DOIs
StatePublished - 1977

ASJC Scopus subject areas

  • Mathematics(all)

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