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.


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