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arXiv · 2403.02174

On Hilbert's 16th Problem

Lars Andersen
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Abstract

We prove that to each real singularity $f: (\mathbb{R}^{n}, 0) \to (\mathbb{R}^k, 0)$ with $k\geq 2$ one can associate systems of differential equations $\mathfrak{g}^{k}_f$ which are pushforwards in the category of $\mathcal{D}$-modules over $\mathbb{R}^{k}$ 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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Lars Andersen. 2024-03-04. On Hilbert's 16th Problem. https://arxiv.org/abs/2403.02174

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