In this paper we study a Fermi–Ulam model where a pingpong ball bounces elastically against a periodically oscillating platform in a gravity field. We assume that the platform motion $f(t)$ is 1-periodic and piecewise $C^3$ with a singularity, $\dot {f}(0+)\ne \dot {f}(1-)$ . If the second derivative $\ddot {f}(t)$ of the platform motion is either always positive or always less than $-g$ , where g is the gravitational constant, then the escaping orbits constitute a null set and the system is recurrent. However, under these assumptions, escaping orbits co-exist with bounded orbits at arbitrarily high energy levels.

在本文中，我们研究了费米-乌拉姆模型，其中乒乓球在重力场中对周期性振荡的平台弹性反弹。我们假设平台运动 $f(t)$ 是 1 周期和分段 $C^3$ 具有奇点 $\dot {f}(0+)\ne \dot {f}(1-)$ 。如果平台运动的二阶导数 $\ddot {f}(t)$ 要么总是正的要么总是小于 $-g$ ，其中g是引力常数，那么逃逸轨道构成一个零集，系统是反复发作。然而，在这些假设下，逃逸轨道与任意高能级的有界轨道共存。