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arXiv math/02070062002-07-01math.DSmath.CV

Exponentially long time stability for non--linearizable analytic germs of $(\C^n,0)$

Timoteo Carletti

备注：: 10 pages

英文摘要：

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.

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