R. de la Llave
Invariant manifolds associated to non-resonant 
spectral subspaces.
(88K, TeX)

ABSTRACT.  We show that, if the linearization of a map at a fixed point leaves
invariant a spectral subspace  which satisfies certain  non-resonance
conditions, the map leaves invariant a smooth manifold tangent to this
subspace.  This manifold is as smooth as the map, but is unique among
$C^L$ invariant manifolds, where $L$ depends only on the spectrum of
the linearization.  We show that if the non-resonance conditions are
not satisfied, a smooth invariant manifold need not  exist and also
establish smooth dependence on parameters.  We also discuss some
applications of these invariant manifolds and briefly survey related
work.