Methods of finding periodic orbit in chaotic systems

Abstract

The dynamics of a chaotic system is full of chaotic orbits, especially for highe r levels where resonances are strong enough to destroy most periodic and/or quas iperiodic trajectories.Though the remnant periodic orbits are scarce,they are no t to be neglected because they form the invariant skeleton of the dynamical phas e space.For instance,we can quantize a nonintegrable system by its periodic orbi ts,which implies the important role of periodic orbits.Therefore,the locating of periodic orbits becomes one of the key points in the study of the dynamics of c haotic systems.Based on explicit examples,we list three methods for locating the periodic orbits in this paper,and conclude that the Newton method is the optima l choice.