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Lemma 2.3
Under a hamiltonian deformation J d h ~ J\,\widetilde{\!dh\,} L L
d d t θ \displaystyle{d\over dt}\theta\! = \displaystyle= − Δ L ( h ) , \displaystyle\!-\Delta_{L}(h), (2.4)
d d t vol L \displaystyle{d\over dt}\vol_{L}\! = \displaystyle= − ⟨ d θ , d h ⟩ vol L . \displaystyle\!-\langle d\theta,dh\rangle\vol_{L}.