Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings
Exactly Solvable and Integrable Systems
2009-11-11 v1
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.
Keywords
Cite
@article{arxiv.nlin/0603005,
title = {Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings},
author = {Hironori Inoue and Daisuke Takahashi and Junta Matsukidaira},
journal= {arXiv preprint arXiv:nlin/0603005},
year = {2009}
}
Comments
submitted to Physica D