Diffusion and chaos in a bouncing ball model

Abstract

We consider the vertical motion of a free falling ball bouncing elastically on a racket moving in the vertical direction according to a regular periodic function $f$. We give a sufficient condition on the second derivative of $f$ giving motions with arbitrarily large amplitude and chaotic dynamics in the sense of positive entropy. We get the results by breaking many invariant curves of the corresponding map using converse KAM techniques.

References in corpus (3)

• Coexistence of bounded and unbounded motions in a bouncing ball model
• A mechanical counterexample to KAM theory with low regularity
• Chaotic dynamics in an impact problem