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Optimal linearization of vector fields on the torus in non-analytic Gevrey classes

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.issued2022
dc.identifier.issn1873-1430
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22156
dc.language.isoenen
dc.subjectGevrey classes
dc.subject.ddc515en
dc.titleOptimal linearization of vector fields on the torus in non-analytic Gevrey classes
dc.typeArticle accepté pour publication ou publié
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..
dc.publisher.cityParisen
dc.relation.isversionofjnlnameAnnales de l'Institut Henri Poincaré (C) Analyse non linéaire
dc.relation.isversionofjnlvol39
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2022
dc.relation.isversionofjnlpages501–528
dc.relation.isversionofdoi10.4171/AIHPC/12
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelAnalyseen
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2023-02-04T13:10:51Z
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