We consider the vertical motion of a free falling ball bouncing elastically on a racket moving in the vertical direction according to a regular periodic function f. We give a sufficient condition on the second derivative of f giving motions with arbitrarily large amplitude and chaotic dynamics in the sense of positive entropy. We get the results by breaking many invariant curves of the corresponding map using converse KAM techniques.

中文翻译：

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弹跳球模型中的扩散和混沌

我们考虑自由落球的垂直运动，它根据规则的周期函数f在垂直方向运动的球拍上弹性反弹。在正熵的意义上，我们给出了f的二阶导数给出充分大的条件的运动，该运动具有任意大的振幅和混沌动力学。我们使用逆向KAM技术通过打破相应地图的许多不变曲线来获得结果。