A Poincar\'e-Bendixson theorem for meromorphic connections on Riemann surfaces
Complex Variables
2014-06-27 v1 Dynamical Systems
Abstract
We prove a Poincar\'e-Bendixson theorem describing the asymptotic behavior of geodesics for a meromorphic connection on a compact Riemann surface. We shall also briefly discuss the case of non-compact Riemann surfaces, and study in detail the geodesics for a holomorphic connection on a complex torus.
Cite
@article{arxiv.1406.6944,
title = {A Poincar\'e-Bendixson theorem for meromorphic connections on Riemann surfaces},
author = {Marco Abate and Fabrizio Bianchi},
journal= {arXiv preprint arXiv:1406.6944},
year = {2014}
}