Progressi Recenti in Geometria Reale e Complessa - IX

A Poincaré-Bendixson theorem for meromorphic connections on Riemann surfaces

Fabrizio Bianchi (Università di Pisa)

20 oct 2014 -- 15:30

Levico Terme

Abstract.

One of the main open problems in local dynamics of several complex variables is the understanding of the dynamics of holomorphic germs tangent to the identity in a full neighbourhood of the origin. Following the work of M. Abate, F. Bracci and F. Tovena, I shall explain how this problem naturally leads to studying the geodesics for a meromorphic connection on the leaves of some foliation in Riemannian surfaces of a projective space and then present a theorem describing the asymptotic behaviour of such geodesics. This is a joint work with Marco Abate.

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