  We investigate the asymptotic distributions of periodically driven anharmonic
Langevin systems. Utilizing the underlying $SL_2$ symmetry of the Langevin
dynamics, we develop a perturbative scheme in which the effect of periodic
driving can be treated nonperturbatively to any order of perturbation in
anharmonicity. We spell out the conditions under which the asymptotic
distributions exist and are periodic, and show that the distributions can be
determined exactly in terms of the solutions of the associated Hill equations.
We further find that the oscillating states of these driven systems are stable
against anharmonic perturbations.
