Numerical study of a random dynamical system with two degrees of freedom

The classical situation of dynamical systems with two degrees of freedom is completely modified by the introduction of a stochastic element which provides a slow dissolution of the zone of stability. Using a Fokker-Planck method it has been shown that the Gambler's ruin problem is a rather good approximation of the diffusion process. Furthermore the orbits exhibit a C-system character even during the diffusion process. (Auth.)