Exponentially long time stability for non-linearizable analytic germs of ( n ,0).
[Temps de stabilité exponentiellement longs pour les germes analytiques de ( n ,0) non linéarisables.]
Annales de l'Institut Fourier, Tome 54 (2004) no. 4, pp. 989-1004.

Nous étudions le problème du centre de Siegel-Schröder, sur la linéarisation de germes analytiques de plusieurs variables complexes, dans la catégorie Gevrey-s. 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-s. 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-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.

DOI : 10.5802/aif.2040
Classification : 37F50, 70H14
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
Carletti, Timoteo 1

1 Scuola Normale Superiore, piazza dei Cavalieri 7, 56126 Pisa (Italie)
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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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