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Analytic \(k\)-linearizability of some resonant Poisson structures. (English) Zbl 1024.53050

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.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
37G05 Normal forms for dynamical systems

Citations:

Zbl 0728.58011
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