Symplectomorphism refers to a specific type of mapping between symplectic manifolds that preserves the symplectic structure. In more detail, a symplectic manifold is a smooth manifold \( M \) equipped with a closed non-degenerate 2-form \( \omega \), known as the symplectic form. This form allows one to define a geometry that is particularly important in the context of Hamiltonian mechanics and classical physics.
