Global branching of solutions to ODEs and integrability
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910837943304192 |
|---|---|
| author | Halburd, Rod |
| author_facet | Halburd, Rod |
| contents | We consider a natural generalisation of the Painlevé property and use it to identify the known integrable cases of the Lane-Emden equation with a real positive index. We classify certain first-order ordinary differential equations with this property and find necessary conditions for a large family of second-order equations. We consider ODEs such that, given any simply connected domain $Ω$ not containing fixed singularities of the equation, the Riemann surface of any solution obtained by analytic continuation along curves in $Ω$ has a finite number of sheets over $Ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global branching of solutions to ODEs and integrability Halburd, Rod Exactly Solvable and Integrable Systems Complex Variables 34M04 (Primary) 34M55 (Secondary) We consider a natural generalisation of the Painlevé property and use it to identify the known integrable cases of the Lane-Emden equation with a real positive index. We classify certain first-order ordinary differential equations with this property and find necessary conditions for a large family of second-order equations. We consider ODEs such that, given any simply connected domain $Ω$ not containing fixed singularities of the equation, the Riemann surface of any solution obtained by analytic continuation along curves in $Ω$ has a finite number of sheets over $Ω$. |
| title | Global branching of solutions to ODEs and integrability |
| topic | Exactly Solvable and Integrable Systems Complex Variables 34M04 (Primary) 34M55 (Secondary) |
| url | https://arxiv.org/abs/2502.15103 |