An efficient geometric integrator is proposed for solving the perturbed
Kepler motion. This method is stable and accurate over long integration time,
which makes it appropriate for treating problems in astrophysics, like solar
system simulations, and atomic and molecular physics, like classical
simulations of highly excited atoms in external fields. The key idea is to
decompose the hamiltonian in solvable parts and propagate the system according
to each term. Two case studies, the Kepler atom in an uniform field and in a
monochromatic field, are presented and the errors are analyzed.Comment: 17 pages, 5 figures, submitted to the Journal of Computational
Physic