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In this article we investigate the natural domain of definition of a holonomymap associated to a singular holomorphic foliation of the complex projectiveplane. We prove that germs of holonomy between algebraic curves can have largesets of singularities for the analytic continuation. In the Riccati context weprovide examples with natural boundary and maximal sets of singularities. Inthe generic case we provide examples having at least a Cantor set ofsingularities and even a nonempty open set of singularities. The examplesprovided are based on the presence of sufficiently rich contracting dynamics inthe holonomy pseudogroup of the foliation.

Singular sets of holonomy maps for algebraic foliations