On Hilbert's 16th Problem

We prove that to each real singularity $f:({\mathbb{R}}^n,0)\to ({\mathbb{R}}^k,0)$ with $k\ge 2$ one can associate systems of differential equations ${\mathfrak{g}}_f^k$ 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.