Singular sets of holonomy maps for algebraic foliations
Dynamical Systems
2014-04-22 v2 Complex Variables
Abstract
In this article we investigate the natural domain of definition of a holonomy map associated to a singular holomorphic foliation of the complex projective plane. We prove that germs of holonomy between algebraic curves can have large sets of singularities for the analytic continuation. In the Riccati context we provide examples with natural boundary and maximal sets of singularities. In the generic case we provide examples having at least a Cantor set of singularities and even a nonempty open set of singularities. The examples provided are based on the presence of sufficiently rich contracting dynamics in the holonomy pseudogroup of the foliation.
Cite
@article{arxiv.1005.5094,
title = {Singular sets of holonomy maps for algebraic foliations},
author = {Gabriel Calsamiglia and Bertrand Deroin and Sidney Frankel and Adolfo Guillot},
journal= {arXiv preprint arXiv:1005.5094},
year = {2014}
}
Comments
30 pages with 3 figures