论文标题
在弹跳球模型中有界和无限动作的共存
Coexistence of bounded and unbounded motions in a bouncing ball model
论文作者
论文摘要
我们考虑描述球在壁上恒定加速并弹性反射的球的垂直运动的模型。该墙应该根据给定的定期功能$ f $在垂直方向上移动。我们将Aubry-Ather理论应用于生成函数，以证明在弹跳之间具有平均平均时间的有界运动的存在。由于已知无限动作的存在，因此可以找到一类允许有界和无限动作的函数$ f $。
We consider the model describing the vertical motion of a ball falling with constant acceleration on a wall and elastically reflected. The wall is supposed to move in the vertical direction according to a given periodic function $f$. We apply the Aubry-Mather theory to the generating function in order to prove the existence of bounded motions with prescribed mean time between the bounces. As the existence of unbounded motions is known, it is possible to find a class of functions $f$ that allow both bounded and unbounded motions.
