Exponential Fermi Acceleration in a Switching Billiard

In this paper we show the existence of an infinite measure set of exponentially escaping orbits for a resonant Fermi accelerator, which is realised as a square billiard with a periodically oscillating platform. We use normal forms to describe the energy change in a period and employ techniques from the theory of hyperbolic systems with singularities to show the exponential drift given by these normal forms on a divided time-energy phase.