On periodic mappings arising from the QRT system

Atsushi Nobe*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


An eight-parameter family of two-dimensional piecewise linear mappings is discussed. Since the dynamical system is obtained from the QRT system through the ultradiscretization, the dynamical system is called the ultradiscrete QRT system. The ultradiscrete QRT system is considered to be integrable because it has an eight-parameter family of invariant curves which fills the plane. It is shown that, for particular parameters, the dynamical system can be regarded as a dynamical system on a fan associated with the conserved quantity. It is also shown that such a dynamical system has periodic solutions for any initial value. Therefore we call such a dynamical system the ultradiscrete periodic QRT system. From the ultradiscrete periodic QRT system, the periodic QRT system is obtained in terms of the inverse ultradiscretization.

Original languageEnglish
Pages (from-to)229-237
Number of pages9
JournalTheoretical and Applied Mechanics Japan
Publication statusPublished - 2003
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Condensed Matter Physics
  • Mechanics of Materials


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