Resonant phenomena in slowly perturbed elliptic billiards

Abstract

We consider an elliptic billiard whose shape slowly changes. During slow evolution of the billiard certain resonance conditions can be fulfilled. We study the phenomena of capture into a resonance and scattering on resonances which lead to the destruction of the adiabatic invariance in the system.

Comments to ver. 1: This is an improved and corrected version of a paper recently published in Regular & Chaotic Dynamics. Comments to ver. 2: Compared to version 1, the figures were incorporated into manuscript file for convenience, no other changes