Escaping orbits are also rare in the almost periodic Fermi-Ulam ping-pong

TL;DR

This paper investigates the Fermi-Ulam ping-pong problem with almost periodic forcing and finds that escaping orbits are extremely rare, occupying a measure-zero set of initial conditions.

Contribution

It demonstrates that in the almost periodic Fermi-Ulam model, escaping orbits are typically negligible in measure, extending understanding of dynamical behavior under almost periodic forcing.

Findings

Escaping orbits have Lebesgue measure zero in the model.

Almost periodic forcing leads to predominantly non-escaping dynamics.

The measure-zero set of escaping orbits indicates their rarity.

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.