Non-integrability of the Sasano system of type $A^{(2)}_5$

Tsvetana Stoyanova

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arXiv · 2512.01767

Non-integrability of the Sasano system of type $A^{(2)}_5$

Tsvetana Stoyanova

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Abstract

The Sasano sytem of type $A^{(2)}_5$ is a four-dimensional non-linear system of ordinary differential equations, which has an affine Weyl group of symmetries of type $A^{(2)}_5$. It is also a tipe dependent Hamiltonian system, which can be considered as coupled Painlevé III systems. In this paper, utilizing the Morales-Ramis-Simó theory for integrability of Hamiltonian systems, we prove rigorously that for all values of the parameters, for which the Sasano system of type $A^{(2)}_5$ admits a particular rational solution, it is non-integrable by rational first integrals.

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Tsvetana Stoyanova. 2025-12-01. Non-integrability of the Sasano system of type $A^{(2)}_5$. https://arxiv.org/abs/2512.01767

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