Shilnikov lemma for a nondegenerate critical manifold of a Hamiltonian system

We consider a Hamiltonian system possessing a nondegenerate normally hyperbolic symplectic critical manifold $M$ and prove an analog of Shilnikov lemma (or strong $lambda$-lemma). We use it to show that certain chains of heteroclinic orbits to $M$ can be shadowed by a trajectory with energy $H$ close to $H|_M$. This is a generalization of a theorem of Shilnikov and Turayev.
Applications to the Poincar"e second species solutions of the 3 body problem will be given.
The talk will be held in Russian.