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Ck centre unstable manifolds*

Published online by Cambridge University Press:  14 November 2011

Shui-Nee Chow  and
Ke ning Lu
Shui-Nee Chow
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, U.S.A.
Ke ning Lu
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, U.S.A.
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Synopsis

We consider the existence and smoothness of global centre unstable manifolds for finite and infinite dimensional flows or maps. We show that every global centre unstable manifold can be expressed as a graph of a Ck map, provided that the nonlinearities are Ck smooth. The proofs are based on a lemma by D. Henry on a necessary and sufficient condition for a Lipschitz map to be continuously differentiable.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 108 , Issue 3-4 , 1988 , pp. 303 - 320
Copyright
Copyright © Royal Society of Edinburgh 1988

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