University of Minnesota
School of Mathematics


A New Proof of the Stable Manifold Theorem

Richard McGehee and Evelyn Sander

Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 47 (1996), 497-513. doi:


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.

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The original preprint was posted on October 3, 1995, at the Geometry Center as GCG 88. The Geometry Center Website is maintained now at the University of Illinois.
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Last update: May 26, 2018 ©2018 Richard McGehee