Transition to chaos for random dynamical systems

We study the transition to chaos for random dynamical systems. Near the transition, on the chaotic side, the long-time particle distribution (which is fractal) that evolves from an initial smooth distribution exhibits an extreme form of temporally intermittent bursting whose scaling we investigate. As a physical example, the problem of the distribution of particles floating on the surface of a fluid whose flow velocity has a complicated time dependence is considered.