We prove an analog of Shilnikov Lemma for a normally hyperbolic symplectic
critical manifold MâHâ1(0) of a Hamiltonian system. Using this
result, trajectories with small energy H=Ό>0 shadowing chains of homoclinic
orbits to M are represented as extremals of a discrete variational problem,
and their existence is proved. This paper is motivated by applications to the
Poincar\'e second species solutions of the 3 body problem with 2 masses small
of order ÎŒ. As ÎŒâ0, double collisions of small bodies correspond to
a symplectic critical manifold of the regularized Hamiltonian system