  We investigate the classical scattering dynamics of the driven elliptical
billiard. Two fundamental scattering mechanisms are identified and employed to
understand the rich behavior of the escape rate. A long-time algebraic decay
which can be tuned by varying the driving amplitude is established. Pulsed
escape rates and decelerated escaping particles are generic properties of the
harmonically breathing billiard. This suggests time-dependent billiards as
prototype systems to study the nonequilibrium evolution of classical ensembles
encountering a multitude of scattering processes off driven targets.
