论文标题
在真正的分析弹跳问题中的无限动作上
On unbounded motions in a real analytic bouncing ball problem
论文作者
论文摘要
我们认为，根据给定的定期功能$ f（t）$，我们考虑在垂直方向移动的球拍上弹性弹跳的模型。重力力在球上起作用。我们证明，如果函数$ f（t）$属于一类三角学$ 2 $的三角多项式，那么就存在一个初始条件的一维连续性，因此球的速度倾向于无限。我们的结果通过pustyl'nikov改善了前一个，并为KAM理论对该模型的适用性提供了新的上限。
We consider the model of a ball elastically bouncing on a racket moving in the vertical direction according to a given periodic function $f(t)$. The gravity force is acting on the ball. We prove that if the function $f(t)$ belongs to a class of trigonometric polynomials of degree $2$ then there exists a one dimensional continuum of initial conditions for which the velocity of the ball tends to infinity. Our result improves a previous one by Pustyl'nikov and gives a new upper bound to the applicability of KAM theory to this model.
