Randomness in the bouncing ball dynamics

The dynamics of a vibrated bouncing ball is studied numerically in the reduced impact representation, where the velocity of the bouncing ball is sampled at each impact with the plate (asynchronous sampling). Its random nature is thus fully revealed: (i) the chattering mechanism, through which the ball gets locked on the plate, is accomplished within a limited interval of the plate oscillation phase, and (ii) is well described in impact representation by a special structure of looped, nested bands and (iii) chattering trajectories and strange attractors may coexist for appropriate ranges of the parameter values. Structure and substructure of the chattering bands are well explained in terms of a simple impact map rule. These results are of potential application to the analysis of high-temperature vibrated granular gases.