Computing periodic orbits using the anti-integrable limit
chao-dyn
2020-06-02 v1 Chaotic Dynamics
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.
Cite
@article{arxiv.chao-dyn/9802014,
title = {Computing periodic orbits using the anti-integrable limit},
author = {D. G. Sterling and J. D. Meiss},
journal= {arXiv preprint arXiv:chao-dyn/9802014},
year = {2020}
}
Comments
11 Pages Latex2e + 1 Figure (eps). Accepted for publication in Physics Lettes A