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dc.contributor.authorFéjoz, Jacques
dc.date.accessioned2012-04-03T08:24:07Z
dc.date.available2012-04-03T08:24:07Z
dc.date.issued2002
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/8711
dc.language.isoenen
dc.subjectthree-body problemen
dc.subjectsecular systemen
dc.subjectaveragingen
dc.subjectKAM theoremen
dc.subjectregularizationen
dc.subjectsingularityen
dc.subject.ddc515en
dc.titleGlobal Secular Dynamics in the Planar Three-Body Problemen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherNorthwestern University;États-Unis
dc.contributor.editoruniversityotherIMC-CNRS UMR8028;France
dc.description.abstractenWe use the global construction which was made in [6, 7] of the secular systems of the planar three-body problem, with regularized double inner collisions. These normal forms describe the slow deformations of the Keplerian ellipses which each of the bodies would describe if it underwent the universal attraction of only one fictitious other body. They are parametrized by the masses and the semi-major axes of the bodies and are completely integrable on a fixed transversally Cantor set of the parameter space. We study this global integrable dynamics reduced by the symmetry of rotation and determine its bifurcation diagram when the semi-major axes ratio is small enough. In particular it is shown that there are some new secular hyperbolic or elliptic singularities, some of which do not belong to the subset of aligned ellipses. The bifurcation diagram may be used to prove the existence of some new families of 2-, 3- or 4-frequency quasiperiodic motions in the planar three-body problem [7], as well as some drift orbits in the planar n-body problem [8].en
dc.relation.isversionofjnlnameCelestial Mechanics and Dynamical Astronomy
dc.relation.isversionofjnlvol84en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2002
dc.relation.isversionofjnlpages159-195en
dc.relation.isversionofdoihttp://dx.doi.org/10.1023/A:1019969024779en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAnalyseen


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