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

Hironori Inoue, Daisuke Takahashi, Junta Matsukidaira

Research output: Contribution to journalArticle

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)22-30
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Issue number1
Publication statusPublished - 2006 May 1



  • Discrete mapping
  • Integrable system
  • Lyapunov function
  • Ultradiscrete equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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