Seminars: S. V. Bolotin, Shilnikov lemma for a nondegenerate critical manifold of a Hamiltonian system

SEMINARS


Globus Seminar June 5, 2014 15:40, Moscow, IUM (Bolshoi Vlas'evskii per., 11)

Shilnikov lemma for a nondegenerate critical manifold of a Hamiltonian system S. V. Bolotin Steklov Mathematical Institute of Russian Academy of Sciences
Abstract: 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.