ABSTRACT
To end this section, let us show an important link between symplectic diffeomorphisms and Poisson brackets.
PR14 A diffeomorphism f: M ~ N is symplectic iff f preserves the Poisson brackets of functions, that is:
(this last equality following from the Jacobi theorem ifff is a symplectic diffeomorphism) =X f'hrg ={Fg,f·h}.
