Computing periodic orbits using the anti-integrable limit

Abstract

Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. Using the Henon map as an example, we obtain a simple analytical bound on the domain of existence of the horseshoe that is equivalent to the well-known bound of Devaney and Nitecki. We also reformulate the popular method for finding periodic orbits introduced by Biham and Wenzel. Near an anti-integrable limit, we show that this method is guaranteed to converge. This formulation puts the choice of symbolic dynamics, required for the algorithm, on a firm foundation.