Linearization of analytic and non--analytic germs of diffeomorphisms of $({\mathbb C},0)$

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dc.creatorCarletti, T.
dc.creatorMarmi, S.
dc.date2000-03-17
dc.date.accessioned2026-07-07T04:34:21Z
dc.date.available2026-07-07T04:34:21Z
dc.descriptionWe study Siegel's center problem on the linearization of germs of diffeomorphisms in one variable. In addition of the classical problems of formal and analytic linearization, we give sufficient conditions for the linearization to belong to some algebras of ultradifferentiable germs closed under composition and derivation, including Gevrey classes. In the analytic case we give a positive answer to a question of J.-C. Yoccoz on the optimality of the estimates obtained by the classical majorant series method. In the ultradifferentiable case we prove that the Brjuno condition is sufficient for the linearization to belong to the same class of the germ. If one allows the linearization to be less regular than the germ one finds new arithmetical conditions, weaker than the Brjuno condition. We briefly discuss the optimality of our results.
dc.descriptionAMS-Latex2e, 11 pages, in press Bulletin Societe Mathematique de France
dc.identifierhttps://arxiv.org/abs/math/0003105
dc.identifierhttp://arxiv.org/abs/math/0003105
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58866
dc.subjectDynamical Systems
dc.subject05C38, 15A15 (Primary) 05A15, 15A18 (Secondary)
dc.titleLinearization of analytic and non--analytic germs of diffeomorphisms of $({\mathbb C},0)$
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