Accessibility and hyperbolicity

John M. Alongi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We examine conditions under which a point in the stable set of a hyperbolic invariant set for a C1 surface diffeomorphism is accessible via a path from the complement of the stable set. Let M be a surface, and let Λ be a compact saturated hyperbolic locally stably closed invariant set possessing a local product structure. Denote the stable set of Λ by Ws (Λ). Our main result states that z ∈Ws (Λ) is accessible from M \ Ws (Λ) if and only if z lies on the stable manifold of a periodic point p, and there is a branch of a local unstable manifold of p disjoint from Ws (Λ).

Original languageEnglish (US)
Pages (from-to)681-691
Number of pages11
JournalIllinois Journal of Mathematics
Issue number2
StatePublished - 2001

ASJC Scopus subject areas

  • General Mathematics


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