R. de la Llave
Invariant manifolds associated to invariant subspaces without
invariant complements: a graph transform approach
(451K, PS)
ABSTRACT. We use the graph transform method to
prove existence of invariant manifolds near fixed
points of maps tangent to invariant subspaces of
the linearization.
In contrast to the best known of such theorems,
we do not assume that the
corresponding space for the linear map is a spectral subspace.
Indeed, we allow that there is no invariant complement
(in particular, we do not need that the decomposition
corresponds to spectral subspaces).
We also do not need that the spectrum of the
operator restricted to the spaces satisfies the usual
dominance conditions.
We prove some uniqueness theorems and show how
this can be used to prove results for flows.
More general theorems have been proved in \cite{CabreFL02} by
another method.