# On Limit Sets for Geodesics of Meromorphic Connections

@article{Novikov2021OnLS, title={On Limit Sets for Geodesics of Meromorphic Connections}, author={Dmitry Novikov and Boris Z. Shapiro and Guillaume Tahar}, journal={Journal of Dynamical and Control Systems}, year={2021} }

Meromorphic connections on Riemann surfaces originate and are closely related to the classical theory of linear ordinary differential equations with meromorphic coefficients. Limiting behaviour of geodesics of such connections has been studied by e.g. Abate, Bianchi and Tovena [1, 2] in relation with generalized Poincaré-Bendixson theorems. At present, it seems still to be unknown whether some of the theoretically possible asymptotic behaviours of such geodesics really exist. In order to fill…

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