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Partial and complete linearisations at stationary points of infinite-dimensional dynamical systems with foliations and applications*

Published online by Cambridge University Press:  14 November 2011

W. M. Rivera
W. M. Rivera
Affiliation:
CDSNSf†, Georgia Tech, Atlanta, GA 30332; West Georgia College, Carrollton, GA 30118, U.S.A.
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Abstract

In this paper we discuss C1-linearisations of diffeomorphisms and flows on Banach spaces. Strong foliations of the neighbourhood of the fixed point composed of leaves based on successively larger subspaces (similar to those in [14]) are constructed. Generalised gap conditions which involve the width and separation of vertical bands containing the spectrum of a linear operator are imposed to achieve maximal smoothness. The method of proof generalises that of Hartman and of Mora and Solá-Morales. Our theorems apply to weakly coupled systems of damped wave and beam equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 5 , 1996 , pp. 1067 - 1085
Copyright
Copyright © Royal Society of Edinburgh 1996

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