Plane polynomials and Hamiltonian vector fields determined by their singular points

John A. Arredondo, Jesús Muciño-Raymundo

Let $\Sigma (f)$ be critical points of a polynomial $f\in \mathbb{K}[x,y]$ in the plane ${\mathbb{K}}^2$, where $\mathbb{K}$ is $\mathbb{R}$ or $\mathbb{C}$. Our goal is to study the crit…