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Normal forms of Poisson structures with zero 1-jet at a point. (Formes normales de structures de Poisson ayant un 1-jet nul en un point.) (French) Zbl 0958.37021
Summary: Singularities of Poisson structures where 1-jet vanishes appear in a stable manner because they are generically not destroyed by small perturbations of the Poisson structure. In this paper we study these singularities. We give first a normal form for Poisson structures with zero 1-jet but with a “generic” 2-jet at a point. We give also a “quadratisation” result in class \(C^\infty\).

MSC:
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
17B63 Poisson algebras
58K50 Normal forms on manifolds
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