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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
Holomorphic Normal Form of Nonlinear Perturbations of Nilpotent Vector Fields
Laurent Stolovitcha, Freek Verstringeb a CNRS, Laboratoire J.-A. Dieudonné U.M.R. 6621, Université de Nice — Sophia Antipolis, Parc Valrose 06108 Nice Cedex 02, France
b Royal Observatory of Belgium, Ringlaan 3, 1180 Brussels, Belgium
Аннотация:
We consider germs of holomorphic vector fields at a fixed point having a nilpotent linear part at that point, in dimension $n\geqslant 3$. 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 ensures 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 Stróżyna–Żoładek, each such germ is holomorphically conjugate to a Takens normal form. Our proof is based on Newton's method and $\mathfrak{sl}_2(\mathbb C)$-representations.
Ключевые слова:
local analytic dynamics, fixed point, normal form, Belitskii normal form, small divisors, Newton method, analytic invariant manifold, complete integrability.
Образец цитирования:
Laurent Stolovitch, Freek Verstringe, “Holomorphic Normal Form of Nonlinear Perturbations of Nilpotent Vector Fields”, Regul. Chaotic Dyn., 21:4 (2016), 410–436
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd86 https://www.mathnet.ru/rus/rcd/v21/i4/p410
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