On the particle dynamics in a dynamic billiard

We have analyzed the dynamics of a classical point particle experiencing elastic reflection from a single periodically oscillating wall and in a dynamic billiard system with reflections from stationary and oscillating walls. In the case of a single wall, the attachment regime is demonstrated in which the particle is almost localized at the wall during a half-period of oscillations and undergoes multiple reflections from it. It has been shown that, when the parameters of the problem are varied in a range that corresponds to a change in the number of consecutive reflections from the same wall, the dependence of the velocity of the reflected particle on these parameters includes discontinuities of the derivative. For the dynamic billiard system, stable regimes of various types with invariable kinetic energy of the particle, as well as regimes of deterministic chaos, have been considered; in the latter case, these discontinuities also play a significant role.