Sur la normalisation holomorphe de structures de Poisson à 1-jet nul

We show that a Poisson structure whose linear part vanish can be holomorphically normalized in a neighbourhood of its singular point 0∈Cn if on the one hand, a Diophantine condition on a Lie algebra associated to the quadratic part is satisfied, and, on the other hand, the normal form satisfies some formal conditions. To cite this article: P. Lohrmann, C. R. Acad. Sci. Paris, Ser. I 340 (2005).