Source: wikibot/symplectic-manifold
= Symplectic manifold
{wiki=Symplectic_manifold}
A **symplectic manifold** is a smooth manifold \\( M \\) equipped with a closed non-degenerate differential 2-form called the **symplectic form**, typically denoted by \\( \\omega \\). Formally, a symplectic manifold is defined as follows: 1. **Manifold**: \\( M \\) is a differentiable manifold of even dimension, usually denoted as \\( 2n \\), where \\( n \\) is a positive integer.