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.

Growth rates of orbits in non-periodic twist maps and a theorem by Neishtadt

“…Over the last years we have examined the dynamics of twist maps with non-periodic angles [2][3][4][5]. Motivated by the Fermi-Ulam ping-pong model, and also by the Littlewood boundedness problem, we have obtained results on the role of the bounded orbits in the general dynamics [6] and also on the improbability of escaping orbits [7,11,12]. However, the first result for this class of maps is older and due to Neishtadt [9].…”