[Temps de stabilité exponentiellement longs pour les germes analytiques de non linéarisables.]
Nous étudions le problème du centre de Siegel-Schröder, sur la linéarisation de germes analytiques de plusieurs variables complexes, dans la catégorie Gevrey-. Nous introduisons une nouvelle condition arithmétique de type de Bruno, sur la partie linéaire du germe, qui assure l’existence d’une linéarisation formelle Gevrey-. Nous l’utilisons pour démontrer la stabilité effective, c’est-à-dire stabilité pour un temps fini mais long, d’un voisinage du point fixe, pour le germe analytique.
We study the Siegel-Schröder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey-, 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- 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.
Keywords: Siegel center problem, Gevrey class, Bruno condition, effective stability, Nekoroshev like estimates
Mot clés : problème du centre de Siegel, classe Gevrey, condition de Bruno, stabilité effective, estimations type Nekoroshev
@article{AIF_2004__54_4_989_0,
author = {Carletti, Timoteo},
title = {Exponentially long time stability for non-linearizable analytic germs of $({\mathbb {C}}^n,0)$.},
journal = {Annales de l'Institut Fourier},
pages = {989--1004},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {54},
number = {4},
year = {2004},
doi = {10.5802/aif.2040},
mrnumber = {2111018},
zbl = {1063.37043},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2040/}
}
TY - JOUR
AU - Carletti, Timoteo
TI - Exponentially long time stability for non-linearizable analytic germs of $({\mathbb {C}}^n,0)$.
JO - Annales de l'Institut Fourier
PY - 2004
SP - 989
EP - 1004
VL - 54
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PB - Association des Annales de l’institut Fourier
UR - http://www.numdam.org/articles/10.5802/aif.2040/
DO - 10.5802/aif.2040
LA - en
ID - AIF_2004__54_4_989_0
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Carletti, Timoteo. Exponentially long time stability for non-linearizable analytic germs of $({\mathbb {C}}^n,0)$.. Annales de l'Institut Fourier, Tome 54 (2004) no. 4, pp. 989-1004. doi : 10.5802/aif.2040. http://www.numdam.org/articles/10.5802/aif.2040/
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