A map 
between the symplectic
manifolds 
and 
which is a diffeomorphism and 
, where 
is the pullback map induced
by 
(i.e., the derivative of the diffeomorphism 
acting on tangent vectors). A symplectic diffeomorphism is also known as a symplectomorphism
or canonical transformation.
Symplectic Diffeomorphism
See also
Diffeomorphism, Pullback Map, Symplectic ManifoldExplore with Wolfram|Alpha
References
Guillemin, V. and Sternberg, S. Symplectic Techniques in Physics. New York: Cambridge University Press, p. 34, 1984.Referenced on Wolfram|Alpha
Symplectic DiffeomorphismCite this as:
Weisstein, Eric W. "Symplectic Diffeomorphism." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SymplecticDiffeomorphism.html