Classical Dynamics of the Time-Dependent Elliptical Billiard

Abstract

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 non-interacting 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 applying harmonic boundary oscillations 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.

References in corpus (6)

• Ray and wave chaos in asymmetric resonant optical cavities
• Hyperacceleration in a stochastic Fermi-Ulam model
• Open circular billiards and the Riemann hypothesis
• Decay of Classical Chaotic Systems - the Case of the Bunimovich Stadium
• Stadium Billiard with Moving Walls
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Cited by in corpus (7)

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• Computational study of the dynamics of an asymmetric wedge billiard
• Classical dynamics and particle transport in kicked billiards
• Dynamics of a Rotated Orthogonal Gravitational Wedge Billiard