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dc.contributor.authorChenciner, Alain
dc.contributor.authorFéjoz, Jacques
dc.contributor.authorMontgomery, Richard
dc.date.accessioned2011-11-15T13:24:38Z
dc.date.available2011-11-15T13:24:38Z
dc.date.issued2005
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7487
dc.language.isoenen
dc.subjectPeriodic solutionsen
dc.subjectBifurcation problemsen
dc.subjectDynamics of multibody systemsen
dc.subjectFew- and many-body systemsen
dc.subjectNonlinear dynamics and nonlinear dynamical systemsen
dc.subject.ddc515en
dc.titleRotating Eights: I. The three Γi familiesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe show that three families of relative periodic solutions bifurcate out of the Eight solution of the equal-mass three-body problem: the planar Hénon family, the spatial Marchal P12 family and a new spatial family. The Eight, considered as a spatial curve, is invariant under the action of the 24-element group D6 × Z2. The three families correspond to symmetry breakings where the invariance group becomes isomorphic to D6, the three D6s being embedded in the larger group in different ways. The proof of the existence of these three families relies on writing down the action integral in a rotating frame, viewing the angular velocity of the frame as a parameter, exploiting the invariance of the action under a group action which acts on the angular velocities as well as the curves and, finally, checking numerically the non-degeneracy of the Eight. Pictures and numerical evidence of the three families are presented at the end.en
dc.relation.isversionofjnlnameNonlinearity
dc.relation.isversionofjnlvol18en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2005
dc.relation.isversionofjnlpages1407-1424en
dc.relation.isversionofdoihttp://dx.doi.org/10.1088/0951-7715/18/3/024en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherIOP Scienceen
dc.subject.ddclabelAnalyseen


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