Bouncing Ball模型存在马蹄的条件

Existence of the horseshoe for Bouncing Ball mapping

对碰撞恢复系数范围为 0 <α≤ 1的“弹跳球 ( Bouncing Ball)”映射 ,给出了马蹄存在的严格条件 ,既解释了 0 <α<1时的数值结果中的混沌现象 ,同时也减弱了当

In this paper,the strict conditions to the existence of the horseshoe for Bouncing Ball mapping are obtained in the range 0<α≤1 ,where α denotes the coefficient of colliding restitution.The results present explaination to the chaos phenomenon for 0<α<1 in the numerical value research, and decrease the condition of producing chaos for α=1 .