Geometric Proof of Strong Stable/Unstable Manifolds, with Application to   the Restricted Three Body Problem
  We present a method for establishing invariant manifolds for saddle--center fixed points. The method is based on cone conditions, suitably formulated to allow for application in computer assisted proofs, and does not require rigorous integration of the vector field in order to prove the existence of the invariant manifolds. We apply our method to the restricted three body problem and show that for a given choice of the mass parameter, there exists a homoclinic orbit to one of the libration points. 
M. J. Capi\'nski, A. Wasieczko
math.DS