Computing periodic orbits using the anti-integrable limit

D. G. Sterling; J. D. Meiss

doi:10.1016/s0375-9601(98)00094-2

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arXiv · chao-dyn/9802014

Computing periodic orbits using the anti-integrable limit

D. G. Sterling·J. D. Meiss

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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.

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D. G. Sterling, J. D. Meiss. 1998-02-13. Computing periodic orbits using the anti-integrable limit. https://doi.org/10.1016/s0375-9601(98)00094-2

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