TITLE: Stable manifolds associated to fixed points with
linear part equal to identity

AUTHORS:
Inmaculada Baldoma, Ernest Fontich.

Universitat de Barcelona
Departament de Matematica Aplicada i Analisi
Gran Via 585, 08007 Barcelona, Spain

E-mails: immaculada.baldoma@upc.edu, fontich@ub.edu

ABSTRACT:

We consider maps defined on an open set of Rn having a fixed point whose linear
part is the identity. We provide sufficient conditions for the existence of a
stable manifold in terms of the nonlinear part of the map.
These maps arise naturally in some problems of Celestial Mechanics. We apply
the results to prove the existence of parabolic orbits of the spatial elliptic
three-body problem.