On integrals of non-autonomous dynamical systems in finite characteristic
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914318334820352 |
|---|---|
| author | Joshi, Nalini Roffelsen, Pieter |
| author_facet | Joshi, Nalini Roffelsen, Pieter |
| contents | We use a difference Lax form to construct simultaneous integrals of motion of the fourth Painlevé equation and the difference second Painlevé equation over fields with finite characteristic $p>0$. For $p\neq 3$, we show that the integrals can be normalised to be completely invariant under the corresponding extended affine Weyl group action. We show that components of reducible fibres of integrals correspond to reductions to Riccatti equations. We further describe a method to construct non-rational algebraic solutions in a given positive characteristic. We also discuss a projective reduction of the integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09298 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On integrals of non-autonomous dynamical systems in finite characteristic Joshi, Nalini Roffelsen, Pieter Exactly Solvable and Integrable Systems Mathematical Physics 12H05, 33E17, 37P05, 39A10 We use a difference Lax form to construct simultaneous integrals of motion of the fourth Painlevé equation and the difference second Painlevé equation over fields with finite characteristic $p>0$. For $p\neq 3$, we show that the integrals can be normalised to be completely invariant under the corresponding extended affine Weyl group action. We show that components of reducible fibres of integrals correspond to reductions to Riccatti equations. We further describe a method to construct non-rational algebraic solutions in a given positive characteristic. We also discuss a projective reduction of the integrals. |
| title | On integrals of non-autonomous dynamical systems in finite characteristic |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics 12H05, 33E17, 37P05, 39A10 |
| url | https://arxiv.org/abs/2602.09298 |