Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
From Polygons to Ultradiscrete Painlevé Equations
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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From Polygons to Ultradiscrete Painlevé Equations
Інший ID:
2010 Mathematics Subject Classification: 14T05; 14H70; 39A13
DOI:10.3842/SIGMA.2015.056
DOI:10.3842/SIGMA.2015.056
Посилання:
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.
Підтримка:
Christopher M. Ormerod would like to acknowledge Eric Rains for his helpful discussions. Y. Yamada
is supported by JSPS KAKENHI Grant Number 26287018.
Дата:
2015
Переглядів:
535
Завантажень:
262
Анотація:
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.
