Solution to Briot and Bouquet problem on singularities of differential equations

2018/02/10 by Ricardo Pérez-Marco, Perez-Marco, Ricardo
Mathematics · Physics and Astronomy · #37F25 #37F50 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematics and Applications #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1802.03630

openalex publication_date 2018/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Log-Riemann Surfaces

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