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- W61001070 abstract "In this chapter we shall discuss various ways of representing a Poisson structure on a differentiable manifold. Let Mn be a Poisson manifold. The basic remark is the following obvious consequence of (0.4): {f,.} is a derivation of C∞(M). Hence ∀f ∈ C∞(M) there exists a well defined vector field Xf such that $${f,g}= X_f g = - X_g f = dg(X_f) = -df(X_g)$$ (1.1) . Xf will be called the Hamiltonian vector field of f.KeywordsSymplectic ManifoldPoisson StructureDifferentiable ManifoldPoisson ManifoldHamiltonian Vector FieldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
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- W61001070 date "1994-01-01" @default.
- W61001070 modified "2023-09-25" @default.
- W61001070 title "The Poisson Bivector and the Schouten-Nijenhuis Bracket" @default.
- W61001070 doi "https://doi.org/10.1007/978-3-0348-8495-2_2" @default.
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