Symplectic geometry
BRANCH OF DIFFERENTIAL GEOMETRY AND DIFFERENTIAL TOPOLOGY
Symplectic Geometry; Symplectic structure; Symplectic topology
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry was founded by the Russian mathematician Vladimir Arnold and has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold.