An anti-integrable limit of a perturbed canonical McMillan map

We study an infinite perturbation of the canonical McMillan map using anti-integrability by introducing a perturbation in terms of α. For |α|>1, the McMillan map is no longer integrable. We take the anti-integrable (AI) limit of the map by sending two parameters, α and k^, to infinity. At this limit, the map becomes a non-deterministic relation with three solutions, and the dynamics reduce to a subshift on three symbols. Numerical continuation is applied to periodic AI states to continue onto orbits of the full perturbed map. Results show that certain symbolic sequences are more robust than others in the sense that they continue farther away from the AI limit and closer to the integrable McMillan map: self-symmetric sequences and sequences limited to two of the three symbols.