  We consider the model describing the vertical motion of a ball falling with
constant acceleration on a wall and elastically reflected. The wall is supposed
to move in the vertical direction according to a given periodic function $f$.
We apply the Aubry-Mather theory to the generating function in order to prove
the existence of bounded motions with prescribed mean time between the bounces.
As the existence of unbounded motions is known, it is possible to find a class
of functions $f$ that allow both bounded and unbounded motions.
