A new proof of the stable manifold theorem

Richard McGehee; Evelyn Sander

doi:10.1007/BF00914867

A new proof of the stable manifold theorem

Richard McGehee, Evelyn Sander

School of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	497-513
Number of pages	17
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	47
Issue number	4
DOIs	https://doi.org/10.1007/BF00914867
State	Published - Jul 1996

Keywords

Dynamical systems
Invariant manifolds
Iteration
Multivalued maps
Relations

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10.1007/BF00914867

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title = "A new proof of the stable manifold theorem",

abstract = "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.",

keywords = "Dynamical systems, Invariant manifolds, Iteration, Multivalued maps, Relations",

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KW - Dynamical systems

KW - Invariant manifolds

KW - Iteration

KW - Multivalued maps

KW - Relations

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JF - Zeitschrift fur Angewandte Mathematik und Physik

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A new proof of the stable manifold theorem

Abstract

Keywords

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