From Polygons to Ultradiscrete Painlevé Equations

Symmetry Integrability and Geometry-Methods and Applications

article

Christopher Michael Ormerod¹  Yasuhiko Yamada² 

[1] Department of Mathematics, California Institute of Technology;Department of Mathematics, Kobe University

关键词: ultradiscrete;    tropical;    Painlev´e;    QRT;    Cremona;   

DOI  :  10.3842/SIGMA.2015.056

来源: National Academy of Science of Ukraine

【 摘 要 】

The rays of tropical genus one curves are constrained in a way that defines a bounded polygon. When we relax this constraint, the resulting curves do not close, giving rise to a system of spiraling polygons. The piecewise linear transformations that preserve the forms of those rays form tropical rational presentations of groups of affine Weyl type. We present a selection of spiraling polygons with three to eleven sides whose groups of piecewise linear transformations coincide with the Bäcklund transformations and the evolution equations for the ultradiscrete Painlevé equations.

【 授权许可】

Unknown