Transitive decomposition of symmetry groups for the $n$-body problem

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dc.creatorFerrario, Davide L.
dc.date2006-03-29
dc.date.accessioned2026-07-07T07:07:20Z
dc.date.available2026-07-07T07:07:20Z
dc.descriptionPeriodic and quasi-periodic orbits of the $n$-body problem are critical points of the action functional constrained to the Sobolev space of symmetric loops. Variational methods yield collisionless orbits provided the group of symmetries fulfills certain conditions (such as the \emph{rotating circle property}). Here we generalize such conditions to more general group types and show how to constructively classify all groups satisfying such hypothesis, by a decomposition into irreducible transitive components. As examples we show approximate trajectories of some of the resulting symmetric minimizers.
dc.identifierhttps://arxiv.org/abs/math/0603684
dc.identifierhttp://arxiv.org/abs/math/0603684
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110355
dc.subjectDynamical Systems
dc.subject37C80; 70F10
dc.titleTransitive decomposition of symmetry groups for the $n$-body problem
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