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Quasiperiodic motions in the planar three-body problem

dc.contributor.authorFéjoz, Jacques
dc.date.accessioned2012-02-13T11:42:15Z
dc.date.available2012-02-13T11:42:15Z
dc.date.issued2002
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/8135
dc.language.isoenen
dc.subjectthree-body problemen
dc.subjectsecular systemen
dc.subjectaveragingen
dc.subjectregularizationen
dc.subjectKAM theoremen
dc.subjectperiodic orbitsen
dc.subject.ddc515en
dc.titleQuasiperiodic motions in the planar three-body problemen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn the direct product of the phase and parameter spaces, we de ne the perturbing region, where the Hamiltonian of the planar three-body problem is Ck-close to the dynamically degenerate Hamiltonian of two uncoupled two-body problems. In this region, the secular systems are the normal forms that one gets by trying to eliminate the mean anomalies from the perturbing function. They are Pöschel-integrable on a transversally Cantor set. This construction is the starting point for proving the existence of and describing several new families of periodic or quasiperiodic orbits: short periodic orbits associated to some secular singularities, which generalize Poincaré's periodic orbits of the second kind (\Les Méthodes nouvelles de la mécanique céleste", Fi rst Vol., Gauthiers-Villars, Paris, 1892{1899); quasiperiodic motions with three (resp. two) frequencies in a rotating frame of reference, which generalize Arnold's solutions (Russian Math. Survey 18 (1963), 85{191) (resp. Lieberman's solu- tions; Celestial Mech. 3 (1971), 408{426); and three-frequency quasiperiodic motions along which the two inner bodies get arbitrarily close to one another an in nite number of times, generalizing the Chenciner-Llibre's invariant "punc- tured tori" (Ergodic Theory Dynamical Systems 8 (1988), 63{72). The proof relies on a sophisticated version of kam theorem, which itself is proved using a normal form theorem of M. Herman ("Démonstration d'un Théorème de V.I. Arnold," Séminaire de Systèmes Dynamiques and Manuscipts, 1998).en
dc.relation.isversionofjnlnameJournal of Differential Equations
dc.relation.isversionofjnlvol183en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2002
dc.relation.isversionofjnlpages303-341en
dc.relation.isversionofdoihttp://dx.doi.org/10.1006/jdeq.2001.4117en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelAnalyseen


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