Morse index properties of colliding solutions to the $N$-body problem

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dc.creatorBarutello, Vivina
dc.creatorSecchi, Simone
dc.date2006-09-29
dc.date.accessioned2026-07-07T07:25:26Z
dc.date.available2026-07-07T07:25:26Z
dc.descriptionWe study a singular Hamiltonian system with an $\al$-homogeneous potential that contains, as a particular case, the classical $N$--body problem. We introduce a variational Morse--like index for a class of collision solutions and, using the asymptotic estimates near collisions, we prove the non-minimality of some special classes of colliding trajectories under suitable spectral conditions provided $\al$ is sufficiently away from zero. We then prove some minimality results for small values of the parameter $\al$.
dc.identifierhttps://arxiv.org/abs/math/0609837
dc.identifierhttp://arxiv.org/abs/math/0609837
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116714
dc.subjectDynamical Systems
dc.subject37K05; 37B30
dc.titleMorse index properties of colliding solutions to the $N$-body problem
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