96-198 R. de la Llave

Invariant manifolds associated to non-resonant spectral subspaces. (88K, TeX) May 15, 96

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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.

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