  We solve Briot and Bouquet problem (1856) on the existence of non-monodromic
(multivalued) solutions for singularities of differential equations in the
complex domain. The solution is an application of hedgehog dynamics for
indifferent irrational fixed points. We present an important simplification by
only using a local hedgehog for which we give a simpler and direct construction
of quasi-invariant curves which does not rely on complex renormalization.
