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| We consider a Hamiltonian system possessing a normally hyperbolic symplectic manifold $M$ consisting of equilibria
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 an 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 is based on \cite{1,2}.
\begin{thebibliography}{99}
\bibitem{1}
S. Bolotin, P. Negrini, Variational approach to second species periodic solutions of Poincare of the three-body problem. Discrete Contin. Dyn. Syst., 33 (2013), 1009--1032.
\bibitem{2} S. Bolotin, P. Negrini, Shilnikov lemma for a nondegenerate critical manifold of a Hamiltonian system. Regular and Chaotic Dynamics, 18 (2013), 779--805.
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