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The structure of a set of vector fields on Poisson manifolds

2009
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Journal of Physics A: Mathematical and Theoretical
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We show that the Lie bracket of an arbitrary vector field with a Hamiltonian vector field is the sum of a Hamiltonian vector field and an energy-preserving vector field, but that not all vector fields can be so decomposed. PACS number: 45.20.Jj Mathematics Subject Classification: 53D17, 37J05 We present an algebraic property of a set of vector fields on a symplectic or Poisson manifold that, while simple, does not appear in the standard sources (e.g. [1, 2] ). Its novel feature is that it

doi:10.1088/1751-8113/42/14/142001
fatcat:6zz6f3r2ufesbd5nxu6viouybq