Exponentially long time stability for non-linearizable analytic germs of (C^n,0)

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    We study the Siegel-Schröder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey-s, s>0, category. We introduce a new arithmetical condition of Bruno type on the linear part of the given germ, which ensures the existence of a Gevrey-s formal linearization. We use this fact to prove the effective stability, i.e. stability for finite but long time, of neighborhoods of the origin for the analytic germ.
    Original languageEnglish
    Pages (from-to)989-1004
    Number of pages16
    JournalAnnales de l'Institut Fourier
    Issue number4
    Publication statusPublished - 2004


    • Bruno condition
    • Siegel center problem
    • gevrey class
    • effective stability
    • Nekhoreshev like estimates


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