Dynamics of geodesics for meromorphic connections on Riemann surfaces (Karim Rakhimov - Université de Lille)

A classification of the omega limit sets of finitely self-
intersecting geodesics of meromorphic connections on Riemann surfaces is well
studied by Abate, Tovena and Bianchi. The classification of
the omega limit of infinite self-intersecting geodesics left open.

In this talk we study the relation between meromorphic connections and
meromorphic <nobr>k−</nobr>differentials. Moreover, we will give a classification of the
omega limit sets of infinite self-intersecting geodesics of a class of
meromorphic connections.