# symplectic vector field

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 $\mathcal{L}_{X}\omega=0$.

Title symplectic vector field SymplecticVectorField 2013-03-22 13:14:04 2013-03-22 13:14:04 bwebste (988) bwebste (988) 4 bwebste (988) Definition msc 53D05