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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