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# Analytic continuation of holonomy maps of Riccati foliations along Brownian paths

Ponente: Nicolas Hussenot
Institución: Universidade Federal Fluminense, Niteroi, Brasil
Tipo de Evento: Investigación
Cuándo 19/11/2015 de 13:30 a 14:30 Salon de Seminarios Graciela Salicrup vCal iCal

Given an algebraic foliation of the complex projective plane, the study of holonomy maps is of special interest since they encode the dynamical behaviour of its leaves. In this talk, we will be interested in the question of analytic continuation of these holonomy maps. More precisely, we will prove that for a quasi-minimal Riccati foliation, any holonomy germ between complexe projective lines can be analytically continued along a generic Brownian path. The proof will use three main ingredients: the existence of Lyapunov exponents associated with Riccati foliations, the link between Riccati foliations and complex projective structures and the discretization procedure of the Brownian motion.