On periodic mappings arising from the QRT system

Atsushi Nobe*


研究成果: Article査読

4 被引用数 (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.

ジャーナルTheoretical and Applied Mechanics Japan
出版ステータスPublished - 2003

ASJC Scopus subject areas

  • 数学 (全般)
  • 凝縮系物理学
  • 材料力学


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