On quadrirational pentagon maps
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913519026307072 |
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| author | Evripidou, Charalampos Kassotakis, Pavlos Tongas, Anastasios |
| author_facet | Evripidou, Charalampos Kassotakis, Pavlos Tongas, Anastasios |
| contents | We classify rational solutions of a specific type of the set theoretical version of the pentagon equation. That is, we find all quadrirational maps $R:(x,y)\mapsto (u(x,y),v(x,y)),$ where $u, v$ are two rational functions on two arguments, that serve as solutions of the pentagon equation. Furthermore, provided a pentagon map that admits a partial inverse, we obtain genuine entwining pentagon set theoretical solutions. Finally, we show how to obtain Yang-Baxter maps from entwining pentagon maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04945 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On quadrirational pentagon maps Evripidou, Charalampos Kassotakis, Pavlos Tongas, Anastasios Exactly Solvable and Integrable Systems We classify rational solutions of a specific type of the set theoretical version of the pentagon equation. That is, we find all quadrirational maps $R:(x,y)\mapsto (u(x,y),v(x,y)),$ where $u, v$ are two rational functions on two arguments, that serve as solutions of the pentagon equation. Furthermore, provided a pentagon map that admits a partial inverse, we obtain genuine entwining pentagon set theoretical solutions. Finally, we show how to obtain Yang-Baxter maps from entwining pentagon maps. |
| title | On quadrirational pentagon maps |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2405.04945 |