Exponentially long time stability for non-linearizable analytic germs of ( n ,0).
Annales de l'Institut Fourier, Volume 54 (2004) no. 4, p. 989-1004

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.

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.

DOI : https://doi.org/10.5802/aif.2040
Classification:  37F50,  70H14
Keywords: Siegel center problem, Gevrey class, Bruno condition, effective stability, Nekoroshev like estimates
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {4},
     year = {2004},
     pages = {989-1004},
     doi = {10.5802/aif.2040},
     zbl = {1063.37043},
     mrnumber = {2111018},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_4_989_0}
}
Exponentially long time stability for non-linearizable analytic germs of $({\mathbb {C}}^n,0)$.. Annales de l'Institut Fourier, Volume 54 (2004) no. 4, pp. 989-1004. doi : 10.5802/aif.2040. http://www.numdam.org/item/AIF_2004__54_4_989_0/

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