A new proof of the stable manifold theorem

Richard McGehee, Evelyn Sander

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We give a new proof of the stable manifold theorem for hyperbolic fixed points of smooth maps. This proof shows that the local stable and unstable manifolds are projections of a relation obtained as a limit of the graphs of the iterates of the map. The same proof generalizes to the setting of stable and unstable manifolds for smooth relations.

Original languageEnglish (US)
Pages (from-to)497-513
Number of pages17
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number4
StatePublished - Jul 1996


  • Dynamical systems
  • Invariant manifolds
  • Iteration
  • Multivalued maps
  • Relations

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