Stolovitch, Laurent Normal form of commuting vector fields. (Forme normale de champs de vecteurs commutant.) (French) Zbl 0885.58081 C. R. Acad. Sci., Paris, Sér. I 324, No. 6, 665-668 (1997). It is shown that a holomorphic vector field near \(0\in\mathbb{C}^n\) having its positive resonances as first integrals, becomes holomorphically normalizable if it belongs to a commutative Lie algebra of holomorphic vector fields having the same properties. One finds a part of J. Vey’s results (1978-1979) in the Hamiltonian or in the isochore case. Reviewer: G.V.Khmelevskaja-Plotnikova (Namur) Cited in 3 Documents MSC: 37G05 Normal forms for dynamical systems Keywords:normal form; holomorphic commuting vector fields PDFBibTeX XMLCite \textit{L. Stolovitch}, C. R. Acad. Sci., Paris, Sér. I 324, No. 6, 665--668 (1997; Zbl 0885.58081) Full Text: DOI