Timoteo Carletti.
Exponentially long time stability for non--linearizable analytic germs of
$(\C^n,0)$.
(37K, LATeX 2e)

ABSTRACT.  We study the Siegel--Schr\"oder
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.