2013/03/12 by Loïc Teyssier, Teyssier, Loïc
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS
paper · pdf · doi:10.48550/arxiv.1303.2866
arxiv created 2013/11/26 · arxiv updated 2013/11/27
Let F be a germ of a singular foliation of the complex plane. Assuming that F is a generalized curve D. Marin and J.-F. Mattei proved the incompressibility of the foliation in a neighborhood from which a finite set of analytic curves is removed. We show in the present work that this hypothesis cannot be eluded by building examples of foliations, reduced after one blow-up, for which the property does not hold. Even if we manage to prove that the individual saddle-node foliation is incompressible, their leaves not retracting tangentially on the boundary of the domain of definition forbids a generalization of Marin--Mattei's construction. We finally characterize those foliations for which the construction of Marin--Mattei's monodromy can be carried out.