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Spectral sequences and normal forms of Lie algebras of vector fields. (English. Russian original) Zbl 0552.58008
Russ. Math. Surv. 38, No. 5, 152-153 (1983); translation from Usp. Mat. Nauk 38, No. 5(233), 199-200 (1983).
Given a representation $$\alpha$$ of a Lie algebra $${\mathcal G}$$ into the Lie algebra $${\mathcal D}$$ of vector fields together with a suitable filtration of $${\mathcal D}$$, the author constructs a spectral sequence which allows one to calculate a normal form for the elements of $$\alpha$$ ($${\mathcal G})$$ near their elementary critical points. This results applies, for example, when $${\mathcal G}$$ is the Lie algebra of Hamiltonian (resp. contact) vector fields on a symplectic (resp. contact) manifold.
Reviewer: D.McDuff

##### MSC:
 58C25 Differentiable maps on manifolds 58K99 Theory of singularities and catastrophe theory
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