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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.15103 |
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Table of 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 $Ω$.