From Polygons to Ultradiscrete Painlevé Equations

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2015
• Main Authors: Ormerod, C.M., Yamada, Y.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147126
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: From Polygons to Ultradiscrete Painlevé Equations / C.M. Ormerod, Y. Yamada // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 54 назв. — англ.

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 rat...