PlanetMath: symplectic vector field

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symplectic vector field

(Definition)

If $(M,\omega )$ is a symplectic manifold, then a vector field $X\in\mathfrak{X}(M)$ is symplectic if its flow preserves the symplectic structure. That is, if the Lie derivative $\mathcal{L}_X\omega =0$ .

"symplectic vector field" is owned by bwebste.

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Cross-references: Lie derivative, structure, preserves, flow, vector field, symplectic manifold
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This is version 1 of symplectic vector field, born on 2002-12-09.
Object id is 3705, canonical name is SymplecticVectorField.
Accessed 1970 times total.

Classification:

53D05 (Differential geometry :: Symplectic geometry, contact geometry :: Symplectic manifolds, general)

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