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 Crconjugate. 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.
|Original language||English (US)|
|Number of pages||17|
|Journal||Proceedings of the Royal Society of Edinburgh: Section A Mathematics|
|State||Published - 1992|
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