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• W2470585585 abstract "We consider germs of holomorphic vector fields at a fixed point having a nilpotent linear part at that point, in dimension $n geq 3$. Based on Belitskii's work, we know that such a vector field is formally conjugate to a (formal) normal form. We give a condition on that normal form which ensure that the normalizing transformation is holomorphic at the fixed point. We shall show that this sufficient condition is a nilpotent version of Bruno's condition (A). In dimension 2, no condition is required since, according to Str{'o}zyna- Zoladek, each such germ is holomorphically conjugate to a Takens normal form. Our proof is based on Newton's method and $frak{sl}_2(Bbb C)$-representations." @default.
• W2470585585 created "2016-07-22" @default.
• W2470585585 creator A5023158127 @default.
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• W2470585585 date "2016-07-01" @default.
• W2470585585 modified "2023-10-12" @default.
• W2470585585 title "Holomorphic normal form of nonlinear perturbations of nilpotent vector fields" @default.
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• W2470585585 doi "https://doi.org/10.1134/s1560354716040031" @default.
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