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We present a method for establishing invariant manifolds for saddle--centerfixed points. The method is based on cone conditions, suitably formulated toallow for application in computer assisted proofs, and does not requirerigorous integration of the vector field in order to prove the existence of theinvariant manifolds. We apply our method to the restricted three body problemand show that for a given choice of the mass parameter, there exists ahomoclinic orbit to one of the libration points.

Geometric Proof of Strong Stable/Unstable Manifolds, with Application to the Restricted Three Body Problem