Detecting unstable periodic orbits in chaotic systems by using an efficient algorithm

How to detect unstable periodic orbits (UPOs) which reside on the chaotic attractors is an important problem in diverse scientific fields. In this paper, we present an efficient algorithm for computing UPOs. It can be applied to any finite dimensional chaotic systems including hyperchaotic systems. We also discuss numerically the converging regions of the algorithm here. The chaotic Henon map is taken as numerical example in the text.