Scaling Invariance in a Time-Dependent Elliptical Billiard

Abstract

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although the static elliptical billiard is an integrable system, after to introduce time-dependent perturbation on the boundary the unlimited energy growth is observed. The behaviour of the average velocity is described using scaling arguments.

References in corpus (2)

• Fermi acceleration and suppression of Fermi acceleration in a time-dependent Lorentz Gas
• Chaotic dynamics of the elliptical stadium billiard in the full parameter space

Cited by in corpus (6)

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• Fermi acceleration in chaotic shape-preserving billiards
• Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion
• Discussing a transition from bounded to unbounded energy in a time-dependent billiard
• Acceleration in a nonplanar time-dependent billiard
• Symmetry breaking in time-dependent billiards