FRACTAL DISTRIBUTION OF FLOATERS ON A FLUID SURFACE AND THE TRANSITION TO CHAOS FOR RANDOM MAPS

The long-time spatial distribution of particles floating on the surface of a confined fluid whose flow velocity has complicated time dependence is considered. It is shown that this distribution can be either a fractal or else can clump at several (or one) discrete points. The transition from the latter type of distribution to the former occurs when the Lyapunov exponent characterizing the particle motion passes through zero from negative values to positive values. The characteristic features of this type of transition are investigated using random maps. It is shown that near the transition there are extremely intermittent temporal fluctuations in the particle cloud, and their scaling with a parameter is elucidated.