Oscillating states of periodically driven anharmonic Langevin systems

We investigate the asymptotic distributions of periodically driven anharmonic Langevin systems. Utilizing underlying ${\text{SL}}_{2}$ symmetry dynamics, we develop a perturbative scheme in which effect periodic driving can be treated nonperturbatively to any order perturbation anharmonicity. spell out conditions under exist and are show that determined exactly terms solutions associated Hill equations. further find oscillating states these systems stable against perturbations.