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The N-body problem

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
hal.structure.identifierInstitut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
dc.contributor.authorFéjoz, Jacques
dc.date.accessioned2018-02-12T14:45:35Z
dc.date.available2018-02-12T14:45:35Z
dc.date.issued2015
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17382
dc.language.isoenen
dc.subjectNewton's equationen
dc.subjectsymmetryen
dc.subjectreductionen
dc.subjectConley-Wintner endomorphismen
dc.subjectstabilityen
dc.subjectplanetary problemen
dc.subjectHill's problemen
dc.subjectcentral configurationen
dc.subjecthomographic motionsen
dc.subjectrelative equilibriaen
dc.subjecthomothetic motionen
dc.subjectperiodic orbiten
dc.subjectPoincaré's classificationen
dc.subjectchoreographyen
dc.subjectfigure-eight solutionen
dc.subjectLagrangian actionen
dc.subjectLagrange-Jacobi identityen
dc.subjectSundman's inequalityen
dc.subjectcollisionen
dc.subjectregularizationen
dc.subjectMarchal-Chenciner's theoremen
dc.subjectnon-collision singularityen
dc.subjectfinal motionsen
dc.subjectChazy's classificationen
dc.subjectintegrabilityen
dc.subjectfirst integralen
dc.subjecttransverse heteroclinic intersectionen
dc.subjectmonodromy groupen
dc.subjectdifferential Galois theoryen
dc.subjectLindstedt seriesen
dc.subjectvon Zeipel seriesen
dc.subjectsmall denominatorsen
dc.subjectBirkhoff seriesen
dc.subjectLagrange and Laplace stability theoremsen
dc.subjectArnold's theoremen
dc.subjectquasi-periodic orbiten
dc.subjectNekhoroshev theoremen
dc.subjectKAM theoryen
dc.subjectinstabilityen
dc.subjectsymbolic dynamicsen
dc.subject.ddc515en
dc.titleThe N-body problemen
dc.typeChapitre d'ouvrage
dc.description.abstractenWe introduce the N-body problem of mathematical celestial mechanics, and discuss its astronomical relevance, its simplest solutions inherited from the two-body problem (called homographic motions and, among them, homothetic motions and relative equilibria), Poincaré's classification of periodic solutions, symmetric solutions and in particular choreographies such as the figure-eight solution, some properties of the global evolution and final motions, Chazy's classification in the three-body problem, some non-integrability results, perturbations series of the planetary problem and a short account on the question of its stability.en
dc.identifier.citationpages126-167en
dc.relation.ispartofseriestitleEncyclopedia of Life Support Systemsen
dc.relation.ispartoftitleCelestial Mechanicsen
dc.relation.ispartofeditorAlessandra Celletti
dc.relation.ispartofpublnameUnescoen
dc.relation.ispartofpublcityParisen
dc.relation.ispartofdate2015
dc.relation.ispartofpages520en
dc.identifier.urlsitehttps://www.ceremade.dauphine.fr/~fejoz/Articles/Fejoz_2014_nbp.pdfen
dc.subject.ddclabelAnalyseen
dc.relation.ispartofisbn978-1-78021-519-8en
dc.relation.forthcomingnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2018-02-12T14:42:08Z
hal.author.functionaut


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