Saved in:
Bibliographic Details
Main Author: Halburd, Rod
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2502.15103
Tags: Add Tag
No Tags, Be the first to tag this record!
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 $Ω$.