The Existence of Aubry–Mather sets for the Fermi–Ulam Model

We consider the Fermi–Ulam model, which can be described as a particle moving freely between two vertical rigid walls; left one being fixed, whereas right moves according to regular periodic function. The is elastically reflected when hitting walls. show that dynamics of model by an area-preserving monotone twist map. Thus, Aubry–Mather sets exist for every rotation number in interval. Consequently, this gives description global behavior, particularly large class and quasiperiodic orbits model.