On Hilbert's 16th Problem

2024/03/04 by Lars Erslev Andersen, Andersen, Lars
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.2403.02174

openalex publication_date 2024/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that to each real singularity f: (ℝⁿ, 0) → (ℝ^k, 0) with k≥ 2 one can associate systems of differential equations \mathfrakg^k_f which are pushforwards in the category of D-modules over ℝ^k of the sheaf of real analytic functions on the total space of the Milnor fibration. We then use this to study Hilbert's 16th problem on polynomial dynamical systems in the plane.

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