Darboux theorem (symplectic geometry)

The Darboux theorem says that every point of a $2n$-dimensional symplectic manifold has local coordinates in which the symplectic form is ${\sum }_{j}d{x}_j\wedge d{y}_j$. Thus symplectic manifolds have no local invariants beyond dimension.

A Darboux chart is a coordinate chart in which a symplectic form becomes the standard symplectic form.