 02284 Timoteo Carletti.
 Exponentially long time stability for nonlinearizable analytic germs of
$(\C^n,0)$.
(37K, LATeX 2e)
Jul 1, 02

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Abstract. We study the SiegelSchr\"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.
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