Analytic continuation of holonomy germs of Riccati foliations along Brownian paths

2013/10/17 by Nicolas Hussenot, Hussenot, Nicolas
Mathematics · #Advanced Differential Equations and Dynamical Systems #Holomorphic and Operator Theory #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1310.4763

Abstract

This paper deals with the question of analytic continuation of holonomy germs of holomorphic foliations. We prove that for a quasi-minimal Riccati foliation of the complex projective plane, any holonomy germ of the foliation between complex projective lines can be analytically continued along a generic Brownian path.

Citations

• Products of Random Matrices

Related

• On the dynamics of Riccati foliations with non parabolic monodromy representations
• Singularities for analytic continuations of holonomy germs of Riccati foliations
• Monodromy and topological classification of germs of holomorphic foliations
• Nondegenerate germs of holomorphic foliations with prescribed holonomy
• On a neighborhood of a torus leaf of a certain class of holomorphic foliations on complex surfaces