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Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings

Hironori Inoue·Daisuke Takahashi·Junta Matsukidaira
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Abstract

We propose discrete mappings of second order that have a discrete analogue of Lyapunov function. The mappings are extensions of the integrable Quispel-Roberts-Thompson (QRT) mapping, and a discrete Lyapunov function of the mappings is identical to an explicit conserved quantity of the QRT mapping. Moreover we can obtain a differential and an ultradiscrete limit of the mappings preserving the existence of Lyapunov function. We also give applications of a mapping with an adjusted parameter, a probabilistic mapping and coupled mappings.

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Hironori Inoue, Daisuke Takahashi, Junta Matsukidaira. 2006-03-01. Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings. https://doi.org/10.1016/j.physd.2006.03.004

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