Mohamed Sami ElBialy
Sub-stable and weak-stable manifolds associated with finitely 
non-resonant spectral decompositions
(162K, AMS-LaTex2e)

ABSTRACT.  In this work we study $C^{k,s}, 2\leq k \leq \infty , 0\leq s \leq 1$, 
maps of a Banach space near a fixed point. We show the existance and 
uniqueness of a class of $C^{k,s}$ local invariant submanifolds of the 
stable manifold which correspond to a spectral subspace satisfying 
a finite non-resonance condition of order $L \leq k$ and an overriding 
condition of order $L\leq k$ (condition (3) of Theorem 1). 
We study the dependence of these invariant manifolds on a parameter 
that lies in a Banach space. 
We also show that a $C^{k,s}, 2\leq k \leq \infty , 0\leq s \leq 1$, 
local weak-stable manifold that satisfies these two conditions is 
unique.