2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97535We 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.10 pagesDynamical SystemsComplex Variables32A05; 37F50; 34E05text