Scaling in stochastic Hamiltonian systems: A renormalization approach

Destabilization of the period-doubling scenario in Hamiltonian systems due to noise is studied. A renormalization picture for stochastic area-preserving maps is introduced and a new universal characteristic number ${\gamma }_{\mathrm{H}=\mathrm{17.017.}\mathrm{}..}$ for the noise amplitude is found. This factor governs scaling properties of the escape time from stable regions, which is demonstrated numerically as well.