Novel temporal behavior of a nonlinear dynamical system: The completely inelastic bouncing ball

Abstract

We consider a ball under the influence of gravity on a vibrating platform where the ball-platform collisions are completely inelastic. We present for the first time several remarkable features in the temporal behavior of the system; its phase space is divided into transmitting and absorbing regions, which are responsible for the abrupt termination of a period-doubling sequence and the onset of a locking regime, in which an appropriately defined winding number has intriguing scaling properties.