Symplectic Diffeomorphism

A Map $T:(M_1,\omega_1)\rightarrow(M_2,\omega_2)$ between the Symplectic Manifolds $(M_1,\omega_1)$ and $(M_2,\omega_2)$ which is a Diffeomorphism and $T^*(\omega_2)=\omega_1$ (where $T^*$ is the Pullback Map induced by $T$, i.e., the derivative of the Diffeomorphism $T$ acting on tangent vectors). A symplectic diffeomorphism is also known as a Symplectomorphism or Canonical Transformation.

See also Diffeomorphism, Pullback Map, Symplectic Manifold

References

Guillemin, V. and Sternberg, S. Symplectic Techniques in Physics. New York: Cambridge University Press, p. 34, 1984.