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Applicable Analysis
An International Journal
Volume 49, 1993 - Issue 1-2
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An abstract approach to smoothness of invariant manifolds

Pages 119-150 | Published online: 02 May 2007
 

Abstract

We establish a general abstract Cm-fixed-point theorem for a finite scale of Banach spaces, extending to the Cm-case a previous C1-fixed-point theorem of Vanderbauwhede and Van Gils. This result gives short proofs of Cm-smoothness for center-, center-unstable, inertial and other center-like invariant manifolds for various types of differential and difference equations in finite and infinite dimensions. It is also applicable to fixed-point equations on LP-spaces. In the present paper we present applications to invariant manifolds for evolution equations with time-dependent nonlinearities.

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