  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.
