Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization

In a recent paper, Stoffer showed that, under a very weak restriction on th e step size, weakly attractive invariant tori of dissipative perturbations of integrable Hamiltonian systems persist under symplectic numerical discre tizations. Stoffer's proof works directly with the discrete scheme. Here, w e show how such a result, together with approximation estimates, can be obt ained by combining Hamiltonian perturbation theory and backward error analy sis of numerical integrators. In addition, we extend Stoffer's result to di ssipative perturbations of nonintegrable Hamiltonian systems in the neighbo rhood of a KAM torus. (C) 1999 Elsevier Science B.V. and IMACS. All rights reserved.