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On "Arnold's theorem" on the stability of the solar system

dc.contributor.authorFéjoz, Jacques
dc.date.accessioned2012-10-15T09:48:16Z
dc.date.available2012-10-15T09:48:16Z
dc.date.issued2013
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10475
dc.language.isoenen
dc.subjectnon-degeneracyen
dc.subjectHerman's resonanceen
dc.subjectresonanceen
dc.subjectsolar systemen
dc.subjectKAMen
dc.subjectstabilityen
dc.subject.ddc520en
dc.titleOn "Arnold's theorem" on the stability of the solar systemen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherInstitut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE) http://www.imcce.fr/ CNRS : UMR8028 – INSU – Observatoire de Paris – Université Paris VI - Pierre et Marie Curie – Université Lille 1 - Sciences et Technologies;France
dc.description.abstractenArnold's theorem on the planetary problem states that, assuming that the masses of n planets are small enough, there exists in the phase space a set of initial conditions of positive Lebesgue measure, leading to quasiperiodic motions with 3n−1 frequencies. Arnold's initial proof is complete only for the plane 2-planet problem. Arnold had missed a resonance later discovered by Herman. The first complete proof, by Herman-Féjoz, relies on the weak non-degeneracy condition of Arnold-Pyartli. A second proof, by Chierchia-Pinzari, is closer to Arnold's initial idea and shows the strong non-degeneracy of the problem after suitable reduction by (part of) the symmetry of rotation. We review and compare these proofs. In an appendix, we define the Poincaré coordinates and prove their symplectic nature through the shortest possible computation.en
dc.relation.isversionofjnlnameDiscrete and Continuous Dynamical Systems. Series A
dc.relation.isversionofjnlvol33
dc.relation.isversionofjnlissue8
dc.relation.isversionofjnldate2013
dc.relation.isversionofjnlpages3555-3565
dc.relation.isversionofdoihttp://dx.doi.org/10.3934/dcds.2013.33.3555
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00741551en
dc.relation.isversionofjnlpublisherAmerican Institute of Mathematical Sciences
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.description.submittednonen


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