Classical dynamics of the time-dependent elliptical billiard

In this work we study the nonlinear dynamics of the static and the driven ellipse. In the static case, we find numerically an asymptotical algebraic decay for the escape of an ensemble of noninteracting particles through a small hole due to the integrable structure of the phase space of the system. Furthermore, for a certain hole position, a saturation value in the decay that can be tuned arbitrarily by varying the eccentricity of the ellipse is observed and explained. When harmonic boundary oscillations are applied, this saturation value, caused by librator-type orbits, is gradually destroyed via two fundamental processes which are discussed in detail. As a result, an amplitude-dependent emission rate is obtained in the long-time behavior of the decay, suggesting that the driven elliptical billiard can be used as a controllable source of particles.