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

Abstract

In this paper, we are concerned with the possibility of bounded growth of the energy of the Fermi–Ulam model in an external gravitational field. The boundedness of all orbits is established when the forced oscillation is almost periodic and real analytic with respect to time. Furthermore, the existence of infinitely many bounded orbits will be proved when the forced oscillation is only supposed to be bounded in the C 2 norm with no other assumptions, and a specifically forced oscillation is constructed such that an unbounded orbit appears.