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

Solution to Briot and Bouquet problem on singularities of differential equations