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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147126 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862715750278496256 |
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| author | Ormerod, C.M. Yamada, Y. |
| author_facet | Ormerod, C.M. Yamada, Y. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T18:00:42Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147126 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:00:42Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ormerod, C.M. Yamada, Y. 2019-02-13T17:08:06Z 2019-02-13T17:08:06Z 2015 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 https://nasplib.isofts.kiev.ua/handle/123456789/147126 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. Christopher M. Ormerod would like to acknowledge Eric Rains for his helpful discussions. Y. Yamada
 is supported by JSPS KAKENHI Grant Number 26287018. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications From Polygons to Ultradiscrete Painlevé Equations Article published earlier |
| spellingShingle | From Polygons to Ultradiscrete Painlevé Equations Ormerod, C.M. Yamada, Y. |
| title | 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_short | From Polygons to Ultradiscrete Painlevé Equations |
| title_sort | from polygons to ultradiscrete painlevé equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147126 |
| work_keys_str_mv | AT ormerodcm frompolygonstoultradiscretepainleveequations AT yamaday frompolygonstoultradiscretepainleveequations |