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Smooth conjugacy of centre manifolds

Published online by Cambridge University Press:  14 November 2011

Almut Burchard ,
Bo Deng  and
Kening Lu
Almut Burchard
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA30332, U.S.A.
Bo Deng
Affiliation:
Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, NE 68588, U.S.A.
Kening Lu
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, U.S.A.
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Synopsis

In this paper, we prove that for a system of ordinary differential equations of class Cr+1,1, r≧0 and two arbitrary Cr+1, 1 local centre manifolds of a given equilibrium point, the equations when restricted to the centre manifolds are Cr conjugate. The same result is proved for similinear parabolic equations. The method is based on the geometric theory of invariant foliations for centre-stable and centre-unstable manifolds.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 1-2 , 1992 , pp. 61 - 77
Copyright
Copyright © Royal Society of Edinburgh 1992

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