Resumen de On Unbounded Motions in a Real Analytic Bouncing ball Problem
We consider the model of a ball elastically bouncing on a racket moving in the vertical direction according to a given periodic function f (t). The gravity force is acting on the ball. We prove that if the function f (t) belongs to a class of trigonometric polynomials of degree 2 then there exists a one dimensional continuum of initial conditions for which the velocity of the ball tends to infinity. Our result improves a previous one by Pustyl’nikov and gives a new upper bound to the applicability of KAM theory to this model.
