  This paper deals with the numerical integration of Hamiltonian systems in
which a stiff anharmonic potential causes highly oscillatory solution behavior
with solution-dependent frequencies. The impulse method, which uses micro- and
macro-steps for the integration of fast and slow parts, respectively, does not
work satisfactorily on such problems. Here it is shown that variants of the
impulse method with suitable projection preserve the actions as adiabatic
invariants and yield accurate approximations, with macro-stepsizes that are not
restricted by the stiffness parameter.
