Basto-Gonçalves, J.; Cruz, I. Analytic \(k\)-linearizability of some resonant Poisson structures. (English) Zbl 1024.53050 Lett. Math. Phys. 49, No. 1, 59-66 (1999). Summary: We consider analytic Poisson tensors \(P\) whose associated Lie algebra at a singular point is resonant (in the sense of J. P. Dufour [J. Differ. Geom. 32, 415-428 (1990; Zbl 0728.58011)]). We give sufficient conditions on the \(k\)-jet of \(P\) at the given point so that \(P\) is analytically linearizable. Cited in 3 Documents MSC: 53D17 Poisson manifolds; Poisson groupoids and algebroids 37G05 Normal forms for dynamical systems Keywords:resonant Poisson structures; singularities; normal forms Citations:Zbl 0728.58011 PDFBibTeX XMLCite \textit{J. Basto-Gonçalves} and \textit{I. Cruz}, Lett. Math. Phys. 49, No. 1, 59--66 (1999; Zbl 1024.53050) Full Text: DOI