A Fast Method to Find Periodic Orbits in Chaotic Attractors With Applications to the Rössler System

A systematic method to find short unstable periodic orbits embedded in chaotic attractors is proposed. The method is based on the construction of symbolic representations of trajectories, which are used to limit the number of symbol sequences considered to find periodic orbits with a given period and also to find candidates of periodic orbits. The Newton method is applied to find accurate positions of periodic orbits. Using the Rössler system as an example, it is shown that the proposed method outperforms existing methods in terms of the number of periodic orbits found and the computation time.