Since the Hamiltonian can be an arbitrary function of x and p, there are such infinitesimal canonical transformations corresponding to every classical quantity G, where G serves as the Hamiltonian to generate a flow of points in phase space for an increment of time s, d x = ∂ ∂ G ∂ ∂ p d s = { G , X } d s d p = − − ∂ ∂ G ∂ ∂ x d s = { G , P } d s .