×

Normal form of commuting vector fields. (Forme normale de champs de vecteurs commutant.) (French) Zbl 0885.58081

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.

MSC:

37G05 Normal forms for dynamical systems
PDFBibTeX XMLCite
Full Text: DOI