Singular sets of holonomy maps for algebraic foliations

Details Singular sets of holonomy maps for algebraic foliations Singular sets of holonomy maps for algebraic foliations

2010-05-27

arxiv.org/abs/1005.5094v2

Mathematics

Dynamical Systems

30 pages with 3 figures

Scientific paper

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.

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