周期受击陀螺系统波函数的分形

摘要

In this paper we study the fractal dimensions of wave function for the periodically kicked free top. We find that when kicking strength coefficient is less than or equal to 1 (6 1), the motion in classical phase space is regular, the fractal dimension is about 1, and as kicking strength increases, the motion in classical phase space becomes chaotic and the fractal dimension also increases. And we also find that when kicking strength is greater than or equal to 6 (>6), the phase space becomes completely chaotic, the fractal dimension reaches its maximum value 1.5 and will keep this value.%研究了周期受击陀螺系统波函数的分形。发现在打击强度系数较弱时(即61时)，相空间是规则的，分形维接近于1；随着打击强度系数的增大，相空间开始变得混沌，分形维也随之增大；当打击强度系数达到6时，相空间完全混沌，分形维将达到最大值，此时若继续增大打击强度系数，分形维保持基本不变。