MPEJ Volume 9, No. 3, 35 pp.
Received: May 23, 2003. Revised: Aug 5, 2003. Accepted: Aug 15, 2003.
R. de la Llave
Invariant manifolds associated to invariant subspaces without
invariant complements: a graph transform approach
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 [CFdlL03a] by another
method.
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