Let $n\in\mathbb N$, let $M$ be a [smooth manifold](/page/Smooth%20Manifold) of dimension $2n$, let $\omega\in\Omega^2(M)$ be a closed nondegenerate smooth $2$-form, and let $x_0\in M$. Then there exist an open neighbourhood $U\subset M$ of $x_0$ and a smooth coordinate chart $\varphi:U\to \varphi(U)\subset \mathbb R^{2n}$ with coordinate functions $(q_1,\dots,q_n,p_1,\dots,p_n)$ such that $\varphi(x_0)=0$ and, as $2$-forms on $U$,

\begin{align*} \omega|_U=\sum_{i=1}^n dq_i\wedge dp_i. \end{align*}

Equivalently, every point of a symplectic manifold has a Darboux chart.