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

Timoteo Carletti

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

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Abstract

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 language	English
Pages (from-to)	989-1004
Number of pages	16
Journal	Annales de l'Institut Fourier
Volume	54
Issue number	4
Publication status	Published - 2004

Keywords

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

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

abstract = "We study the Siegel-Schr{\"o}der 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. ",

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AU - Carletti, Timoteo

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N2 - 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.

AB - 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.

KW - Bruno condition

KW - Siegel center problem

KW - gevrey class

KW - effective stability

KW - Nekhoreshev like estimates

M3 - Article

VL - 54

SP - 989

EP - 1004

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 4

ER -

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

Abstract

Keywords

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