Existence of invariant curves for a Fermi-type impact absorber

In this paper we study an impact absorber which is similar to the Fermi accelerator and can be described as a ball moves in a periodically oscillating ring with a wall and reflects elastically from the wall. First, Poincaré map of the system is established. The existence of invariant curves for the map is proved based on Moser's twist theorem. Accordingly, the velocities of the ball are always bounded for any initial motion for all time. Moreover, the symmetry of the Poincaré map is discussed. Finally, some numerical simulations are given to demonstrate the theoretical results.