From Hamiltonian perturbation theory to symplectic integrators and back Original Research Article

Hamiltonian perturbation theory explains how symplectic integrators work and, in particular, why they can be used to measure extremely small energy exchanges between different degrees of freedom in molecular collision problems. Conversely, numerical experiments based on symplectic integrators permit a detailed understanding of the dynamics of nearly integrable Hamiltonian systems, thus providing a valuable support to Hamiltonian perturbation theory.