02-284 Timoteo Carletti.
Exponentially long time stability for non--linearizable analytic germs of $(\C^n,0)$. (37K, LATeX 2e) Jul 1, 02
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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.

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