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Normalisation holomorphe de structures de Poisson. (English) Zbl 1204.53072
Using [L. Stolovitch, Ergodic Theory and Dyn. Syst. 24, No. 5, 1833–1863 (2004; Zbl 1090.53066)] the author gives sufficient conditions for the holomorphic normalizability of Poisson structures (PS) with vanishing linear part in neighborhood of its singular point \(0 \in \mathbb{C}^n\). These conditions consist in a Diophantine condition on a Lie algebra associated to quadratic part of PS and some restrictions on the normal form.

MSC:
53D17 Poisson manifolds; Poisson groupoids and algebroids
34A26 Geometric methods in ordinary differential equations
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