算法对混沌体系逃逸率的影响

以Hénon-Heiles体系为例，研究算法对混沌体系运动轨道和逃逸率计算结果的影响.比较了新发现的四阶辛算法和一种非辛的高阶算法得到的结果.发现两种算法给出的轨迹之间的距离随时间增大，增加的速度可以作为体系相空间混沌的度量.通过跟踪大数量的粒子轨迹，提取出了逃逸率随体系能量的变化.发现由两种算法得到的逃逸率相互符合得很好. 关键词： 逃逸率 Hénon-Heiles体系 辛算法

Escaping problem in the Hénon-Heiles system and numerical algorithms

We study the trajectories and escaping problem in the Henon-Heiles system using a new fourth order symplectic algorithm and the Runge-Kutta-Fehlberg algorithm. Starting from the same initial point, we found the distance between the two numerical trajectories calculated by the two algorithms increases exponentially in time in the chaotic region. We show this result can be used to measure chaos. We also calculate the escape rate as a function of energy above threshold in the Henon-Heiles system. The results calculated with two different algorithms agree very well.