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Exponentially long time stability for non-linearizable analytic germs of \(({\mathbb C}^n,0)\).. (English) Zbl 1063.37043

Summary: 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.

MSC:

37F50 Small divisors, rotation domains and linearization in holomorphic dynamics
70H14 Stability problems for problems in Hamiltonian and Lagrangian mechanics
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