Dynamics of a ball on a vibrating plate

We study both analytically and numerically the problem of a partially inelastic ball on a platform vibrating with frequency ω. Two parameters control the dynamics, the restitution coefficient η, and the reduced acceleration Γ= γ/g, where γ is the maximum acceleration of the motion of the plate and g the acceleration of gravity. When η exceeds some value, simple stable fixed points no longer exist, but it is shown that generic trajectories are periodic with period TB which behaves as TB ∼(1 - η)-5 for η close to 1.