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

被引：3
|
作者：
Inoue, Hironori
Takahashi, Daisuke
Matsukidaira, Junta
机构：
[1] Waseda Univ, Dept Math Sci, Shinjuku Ku, Tokyo 1698555, Japan
[2] Ryukoku Univ, Dept Appl Math & Informat, Otsu, Shiga 5202194, Japan
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2006年 / 217卷 / 01期
关键词：
discrete mapping; integrable system; Lyapunov function; ultradiscrete equation;
D O I：
10.1016/j.physd.2006.03.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (c) 2006 Elsevier B.V. All rights reserved.
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页码：22 / 30
页数：9
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