Reductions and degenerate limits of Yang-Baxter maps with $3\times 3$ Lax matrices

P. Adamopoulou; T. E. Kouloukas; G. Papamikos

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arXiv · 2501.01210

Reductions and degenerate limits of Yang-Baxter maps with $3\times 3$ Lax matrices

P. Adamopoulou·T. E. Kouloukas·G. Papamikos

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Abstract

We generalise a family of quadrirational parametric Yang-Baxter maps with $3\times 3$ Lax matrices by introducing additional essential parameters. These maps preserve a prescribed Poisson structure which originates from the Sklyanin bracket. We investigate various low-dimensional reductions of this family, as well as degenerate limits with respect to the parameters that were introduced. As a result, we derive several birational Yang-Baxter maps, and we discuss some of their integrability properties. This work is part of a more general classification of Yang-Baxter maps admitting a strong $3\times 3$ Lax matrix with a linear dependence on the spectral parameter.

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P. Adamopoulou, T. E. Kouloukas, G. Papamikos. 2025-01-02. Reductions and degenerate limits of Yang-Baxter maps with $3\times 3$ Lax matrices. https://arxiv.org/abs/2501.01210

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