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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
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S. V. Bolotin


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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.

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