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In this work we study the nonlinear dynamics of the static and the drivenellipse. In the static case, we find numerically an asymptotical algebraicdecay for the escape of an ensemble of non-interacting particles through asmall 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 thatcan be tuned arbitrarily by varying the eccentricity of the ellipse is observedand explained. When applying harmonic boundary oscillations this saturationvalue caused by librator type orbits is gradually destroyed via two fundamentalprocesses which are discussed in detail. As a result, an amplitude dependentemission rate is obtained in the long time behavior of the decay, suggestingthat the driven elliptical billiard can be used as a controllable source ofparticles.

Classical Dynamics of the Time-Dependent Elliptical Billiard