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Singular sets of holonomy maps for algebraic foliations
- Source :
- J Eur Math Soc (JEMS) 15 (2013) no 3 1067-1099
- Publication Year :
- 2010
-
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.<br />Comment: 30 pages with 3 figures
- Subjects :
- Mathematics - Dynamical Systems
Mathematics - Complex Variables
Subjects
Details
- Database :
- arXiv
- Journal :
- J Eur Math Soc (JEMS) 15 (2013) no 3 1067-1099
- Publication Type :
- Report
- Accession number :
- edsarx.1005.5094
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.4171/JEMS/386