Boundedness of solutions for a bouncing ball model with quasiperiodic moving wall

In this work, we consider the model of a free falling ball on a wall that is elastically reflected. The wall is supposed to move in the vertical direction according to a given quasiperiodic function. Based on the invariant curve theorem of smooth quasiperiodic twist map, we prove the boundedness of all solutions and the existence of quasi-periodic solutions for the system.

Automated summary

We study a model where a ball falls freely and bounces elastically off a moving wall that follows a given quasiperiodic function in the vertical direction. Using the invariant curve theorem of smooth quasiperiodic twist map, we establish the boundedness of all solutions and the existence of quasi-periodic solutions for the system.