METHOD FOR COMPUTING LONG PERIODIC-ORBITS OF DYNAMICAL-SYSTEMS

The accurate computation of periodic orbits, particularly those of lon g period, is very important for studying a number of interesting prope rties of dynamical systems. In this paper, we implement a method for c omputing periodic orbits of dynamical systems efficiently and to a hig h degree of accuracy. This method converges rapidly, within relatively large regions of initial conditions, and is independent of the local dynamics near periodic points. The only computable information require d is the signs of various function evaluations carried out during the integration of the equations of motion. Here we apply this method to a Duffing oscillator and illustrate its advantages by comparing it with other widely used perturbation techniques.