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Shilnikov Lemma for a nondegenerate critical manifold of a Hamiltonian system | | Sergey Bolotin
; Piero Negrini
; | | Date: |
21 Aug 2013 | | Abstract: | We prove an analog of Shilnikov Lemma for a normally hyperbolic symplectic
critical manifold $Msubset H^{-1}(0)$ of a Hamiltonian system. Using this
result, trajectories with small energy $H=mu>0$ shadowing chains of homoclinic
orbits to $M$ are represented as extremals of a discrete variational problem,
and their existence is proved. This paper is motivated by applications to the
Poincar’e second species solutions of the 3 body problem with 2 masses small
of order $mu$. As $mu o 0$, double collisions of small bodies correspond to
a symplectic critical manifold of the regularized Hamiltonian system. | | Source: | arXiv, 1308.4604 | | Services: | Forum | Review | PDF | Favorites | |
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