# Anti-Integrability for 3-Dimensional Quadratic Maps

@inproceedings{Hampton2021AntiIntegrabilityF3, title={Anti-Integrability for 3-Dimensional Quadratic Maps}, author={Amanda Hampton and James D. Meiss}, year={2021} }

We study the dynamics of the three-dimensional quadratic diffeomorphism using a concept first introduced thirty years ago for the Frenkel-Kontorova model of condensed matter physics: the anti-integrable (AI) limit. At the traditional AI limit, orbits of a map degenerate to sequences of symbols and the dynamics is reduced to the shift operator, a pure form of chaos. Under nondegeneracy conditions, a contraction mapping argument can show that infinitely many AI states continue to orbits of the…

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