Noun
symplectomorphism (plural symplectomorphisms)
(mathematics) An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure.
In dimension 2, a symplectic manifold is just a surface endowed with an area form and a symplectomorphism is an area-preserving diffeomorphism. Source: Internet
One major example is that the graph of a symplectomorphism in the product symplectic manifold (M M, ω ω) is Lagrangian. Source: Internet