Symplectomorphism

Summary

A symplectomorphism is a diffeomorphism between symplectic manifolds that carries one symplectic form to the other. These maps are the isomorphisms of symplectic geometry. In mechanics they are the canonical transformations, and the time-$t$ maps of Hamiltonian flows are symplectomorphisms. Unlike isometries of a Riemannian manifold, the symplectomorphisms of a symplectic manifold form an infinite-dimensional group.