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.

11 Pages Latex2e + 1 Figure (eps). Accepted for publication in Physics Lettes A

References in corpus (1)

• Unstable Periodic Orbits in the Stadium Billiard

Cited by in corpus (7)

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• A chaotic lattice field theory in one dimension
• Entry and exit sets in the dynamics of area preserving Henon map
• Visualizing Attractors of the Three-Dimensional Generalized Hénon Map
• Anti-Integrability for 3-Dimensional Quadratic Maps