Escaping Orbits Are also Rare in the Almost Periodic Fermi–Ulam Ping-Pong

Abstract

We study the one-dimensional Fermi–Ulam ping-pong problem with a Bohr almost periodic forcing function and show that the set of initial condition leading to escaping orbits typically has Lebesgue measure zero.

Dynamics of the Fermi–Ulam model in an external gravitational field

“…Later, Kunze and Ortega [8] considered the quasi-periodic Fermi-Ulam model with no assumption of the diophantine condition of the frequencies and then proved that escaping orbits are rare, where p is C 2 smooth. Next, Schließauf [14] generalized the result in Kunze and Ortega [8] to the almost periodic case; that is, p is an almost periodic function. The almost periodic function is a generalization of the continuous periodic function.…”