不可积哈密顿系统中寻找不稳定周期轨迹方法

一个混沌系统,由于非线性扰动而遭到破坏时,存活的不稳定周期轨迹体现了体系的本质特征,是体系的运动骨架,因此寻找其不稳定的周期轨迹就是研究非线性系统动力学特性和几何拓扑的关键.本文研究了寻找不稳定周期轨迹的Multipoint Shooting方法,并结合了具体混沌系统实例,探讨了该方法的准确性和高效性.

Methods of Locating Unstable Periodic Orbits in Nonintegrable Hamiltonian Systems

The dynamics of a chaotic system is full of chaotic trajectories due to its stronger resonances which destroy most periodic trajectories.Though the remnant unstable periodic trajectories are scarce,they play important roles in dynamics of a nonlinear system because they form the invariant skeleton of the dynamical phase space,Therefore,the locating of unstable periodic orbits becomes one of the key points in the study of the dynamics and topological structure of the nonlinear systems.Based on explicit examples,the Multipoint Shooting Method for locating the unstable periodic orbits has been studied and its accuracy and higher efficiency have been discussed.