On stabilization of energy for Hamiltonian systems

We study post-stabilization of numerical integrators for an autonomous Hamiltonian system in the form H=H1+H2H=H1+H2, where H1H1 and H2H2 are two constants of motion. It is better to stabilize the two energies H1H1 and H2H2, respectively. As a particular case, the effectiveness of post-stabilization by the total energy is equivalent to one by the two independent energies when the splitting Hamiltonian becomes isotropic.