Method for computing long periodic orbits of dynamical systems

The accurate computation of periodic orbits, particularly those of long period, is very important for studying a number of interesting properties of dynamical systems. In this paper, we implement a method for computing periodic orbits of dynamical systems efficiently and to a high 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 required 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.