关于四边五边形映射

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-05-08 DOI:arxiv-2405.04945

Charalampos Evripidou, Pavlos Kassotakis, Anastasios Tongas

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引用次数: 0

摘要

我们对五边形方程的集合理论转换的特定类型的有理解进行分类。也就是说，我们找到了作为五边形方程解的所有四元映射$R:(x,y)\mapsto (u(x,y),v(x,y))$，其中$u, v$ 是关于两个参数的两个有理函数。此外，只要五边形映射允许部分逆，我们就能得到真正的五边形集理论解。

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On quadrirational pentagon maps

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.

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arXiv - PHYS - Exactly Solvable and Integrable Systems

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