From Polygons to Ultradiscrete Painlevé Equations
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...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2015 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147126 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147126 |
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dspace |
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irk-123456789-1471262019-02-14T01:24:51Z From Polygons to Ultradiscrete Painlevé Equations Ormerod, C.M. Yamada, Y. 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. 2015 Article 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. 1815-0659 2010 Mathematics Subject Classification: 14T05; 14H70; 39A13 DOI:10.3842/SIGMA.2015.056 http://dspace.nbuv.gov.ua/handle/123456789/147126 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Ormerod, C.M. Yamada, Y. |
| spellingShingle |
Ormerod, C.M. Yamada, Y. From Polygons to Ultradiscrete Painlevé Equations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ormerod, C.M. Yamada, Y. |
| author_sort |
Ormerod, C.M. |
| title |
From Polygons to Ultradiscrete Painlevé Equations |
| title_short |
From Polygons to Ultradiscrete Painlevé Equations |
| title_full |
From Polygons to Ultradiscrete Painlevé Equations |
| title_fullStr |
From Polygons to Ultradiscrete Painlevé Equations |
| title_full_unstemmed |
From Polygons to Ultradiscrete Painlevé Equations |
| title_sort |
from polygons to ultradiscrete painlevé equations |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147126 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:26:39Z |
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