A pair (M, ω), where M is a manifold and ω is a symplectic form on M. The phase space R^(2n) = R^n×R^n is a symplectic manifold. Near every point on a symplectic manifold, it is possible to find a set of local "Darboux coordinates" in which the symplectic form has the simple form ω = sum_k d q_k ⋀d p_k (Sjamaar 1996), where d q_k ⋀d p_k is a wedge product.

manifold | symplectic diffeomorphism | symplectic form