Computing periodic orbits using the anti-integrable limit

Details Computing periodic orbits using the anti-integrable limit Computing periodic orbits using the anti-integrable limit

1998-02-13

arxiv.org/abs/chao-dyn/9802014v1

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

10.1016/S0375-9601(98)00094-2

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.

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