Ultradiscrete QRT maps and tropical elliptic curves

Atsushi Nobe*


研究成果: Article査読

15 被引用数 (Scopus)


It is shown that the polygonal invariant curve of the ultradiscrete QRT (uQRT) map, which is a two-dimensional piecewise linear integrable map, is the complement of the tentacles of a tropical elliptic curve on which the curve has a group structure in analogy to classical elliptic curves. Through the addition formula of a tropical elliptic curve, a tropical geometric description of the uQRT map is then presented. This is a natural tropicalization of the geometry of the QRT map found by Tsuda. Moreover, the uQRT map is linearized on the tropical Jacobian of the corresponding tropical elliptic curve in terms of the Abel-Jacobi map. Finally, a formula concerning the period of a point in the uQRT map is given, and an exact solution to its initial-value problem is constructed by using the ultradiscrete elliptic theta function.

ジャーナルJournal of Physics A: Mathematical and Theoretical
出版ステータスPublished - 2008 3月 28

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • モデリングとシミュレーション
  • 数理物理学
  • 物理学および天文学(全般)


「Ultradiscrete QRT maps and tropical elliptic curves」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。