Efficient algorithm for detecting unstable periodic orbits in chaotic systems

We present an efficient method for Fast, complete, and accurate detection o f unstable periodic orbits in chaotic systems. Our method consists of an it erative scheme and an effective technique for selecting initial points. The iterative scheme is based on the semi-implicit Euler method, which has bot h fast and global convergence, and only a small number of initial points is sufficient to detect all unstable periodic orbits of a given period. The p ower of our method is illustrated by numerical examples of both two- and fo ur-dimensional maps. [S1063-651X(99)06711-2].