Escaping problem in the Hénon-Heiles system and numerical algorithms
算法对混沌体系逃逸率的影响

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.