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hal.structure.identifierInstitut de Recherche Mathématique de Rennes [IRMAR]
dc.contributor.authorJézéquel, Tiphaine*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorBernard, Patrick
HAL ID: 281
ORCID: 0000-0001-7250-5604
*
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorLombardi, Eric
HAL ID: 12850
*
dc.date.accessioned2017-11-24T15:19:47Z
dc.date.available2017-11-24T15:19:47Z
dc.date.issued2016
dc.identifier.issn1078-0947
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17042
dc.language.isoenen
dc.subjectNormal forms
dc.subjectexponentially small phenomena
dc.subjectinvariant manifolds
dc.subjectGevrey
dc.subject02iω
dc.subjectHamiltonian systems
dc.subjecthomoclinic orbits with several loops
dc.subjectgeneralized solitary waves
dc.subjectKAM, Liapunoff theorem
dc.subject.ddc519en
dc.titleHomoclinic orbits with many loops near a 02iω resonant fixed point of Hamiltonian systems
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper we study the dynamics near the equilibrium point of a family of Hamiltonian systems in the neighborhood of a 02iω resonance. The existence of a family of periodic orbits surrounding the equilibrium is well-known and we show here the existence of homoclinic connections with several loops for every periodic orbit close to the origin, except the origin itself. The same problem was studied before for reversible non Hamiltonian vector fields, and the splitting of the homoclinic orbits lead to exponentially small terms which prevent the existence of homoclinic connections with one loop to exponentially small periodic orbits. The same phenomenon occurs here but we get round this difficulty thanks to geometric arguments specific to Hamiltonian systems and by studying homoclinic orbits with many loops.
dc.relation.isversionofjnlnameDiscrete and Continuous Dynamical Systems. Series A
dc.relation.isversionofjnlvol36
dc.relation.isversionofjnlissue6
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages3153-3225
dc.relation.isversionofdoi10.3934/dcds.2016.36.xx
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01251087
dc.relation.isversionofjnlpublisherDept. of Mathematics
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-19T10:56:28Z
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