论文标题
撞击问题中的混乱动态
Chaotic dynamics in an impact problem
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 $在垂直方向上移动。我们表明，可以应用基于子和超级溶液的天形方法的修改，以检测混乱的动力学。使用圆柱体的确切符号扭转图理论可以证明在功能$ f $的“自然”条件下的结果。
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 show that a modification of a method of Angenent based on sub and super solutions can be applied in order to detect chaotic dynamics. Using the theory of exact symplectic twist maps of the cylinder one can prove the result under "natural" conditions on the function $f$.
