Non-integrability of the Sasano system of type $A^{(2)}_5$
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911296436305920 |
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| author | Stoyanova, Tsvetana |
| author_facet | Stoyanova, Tsvetana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01767 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-integrability of the Sasano system of type $A^{(2)}_5$ Stoyanova, Tsvetana Exactly Solvable and Integrable Systems Mathematical Physics 34M55, 37J65, 34M40 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. |
| title | Non-integrability of the Sasano system of type $A^{(2)}_5$ |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics 34M55, 37J65, 34M40 |
| url | https://arxiv.org/abs/2512.01767 |