  We call a system bouncing ball billiard if it consists of a particle that is
subjected to a constant vertical force and bounces inelastically on a
one-dimendional vibrating periodically corrugated floor. Here we choose
circular scatterers that are very shallow, hence this billiard is a
deterministic diffusive version of the well-known bouncing ball problem on a
flat vibrating plate. Computer simulations show that the diffusion coefficient
of this system is a highly irregular function of the vibration frequency
exhibiting pronounced maxima whenever there are resonances between the
vibration frequency and the average time of flight of a particle. In addition
there exist irregularities on finer scales that are due to higher-order
dynamical correlations pointing towards a fractal structure of this curve. We
analyze the diffusive dynamics by classifying the attracting sets and by
working out a simple random walk approximation for diffusion, which is
systematically refined by using a Green-Kubo formula.
