On the Qualitative Behaviour of Symplectic Integrators. Part III. Perturbed Integrable Systems

AbstractWe consider a dissipative perturbation of an integrable Hamiltonian system. The perturbed system is assumed to admit a weakly attractive invariant torus. The system is integrated with a symplectic integrator. The discrete system also admits an attractive invariant torus for sufficiently small step-sizes. The step-size may be much larger than the perturbation parameter; it has only to be logarithmically small compared to the perturbation parameter