论文标题
弹跳球模型中的扩散和混乱
Diffusion and chaos in a bouncing ball model
论文作者
论文摘要
我们认为，根据常规周期功能$ f $，我们考虑在垂直方向移动的球拍上弹跳的垂直运动。我们在$ f $的第二个导数中给出了足够的条件，从而在正熵的意义上给出了任意振幅和混乱动态的动作。我们通过使用Converse KAM技术破坏相应地图的许多不变曲线来获得结果。
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.
