Open AccessMethods of finding periodic orbit in chaotic systems
Author(s) -
Peijie Wang,
Guozhen Wu
Publication year - 2005
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.54.3034
Subject(s) - periodic orbits , chaotic , invariant (physics) , orbit (dynamics) , dynamical systems theory , chaotic systems , physics , heteroclinic orbit , classical mechanics , computer science , mathematical physics , bifurcation , homoclinic orbit , quantum mechanics , nonlinear system , aerospace engineering , artificial intelligence , engineering
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.