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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorBounemoura, Abed
dc.date.accessioned2021-11-03T10:13:32Z
dc.date.available2021-11-03T10:13:32Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22156
dc.language.isoenen
dc.subject.ddc515en
dc.titleOptimal linearization of vector fields on the torus in non-analytic Gevrey classesen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe study linear and non-linear small divisors problems in analytic and non-analytic regularity. We observe that the Bruno arithmetic condition, which is usually attached to non-linear analytic problems, can also be characterized as the optimal condition to solve the linear problem in some fixed non quasi-analytic class. Based on this observation, it is natural to conjecture that the optimal arithmetic condition for the linear problem is also optimal for non-linear small divisors problems in any reasonable non quasi-analytic classes. Our main result proves this conjecture in a representative non-linear problem, which is the linearization of vector fields on the torus, in the most representative non quasi-analytic class, which is the Gevrey class. The proof follows Moser's argument of approximation by analytic functions, and uses in an essential way works of Popov, Rüssmann and Pöschel..en
dc.publisher.cityParisen
dc.identifier.citationpages30en
dc.relation.ispartofseriestitleCahier de recherche du CEREMADEen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-03008322en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2020
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2021-11-03T10:10:47Z
hal.author.functionaut


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