Strong λ-lemma and second species periodic solutions of the 3-body problem

Quite recently Bolotin and N. developed a variational approach to the existence of second species periodic solutions for the nonrestricted 3 body problem [2]. An important part of this paper is based on an analog of Shilnikov Lemma (also called strong λ- lemma) for hamiltonian systems possessing a non degenerate normally hyperbolic critical symplectic manifold. The complete proof of the Lemma was postponed to a future publication [3]: in this paper we anticipate a part of the results.