Dulac’s Problem
Let $\xi = (\xi_1,\xi_2):\RR^2 \into \RR^2$ be a vector field of class $C^1$. Recall that the singular set of $\xi$ is the set $$Z(\xi):= \set{z \in \RR^2:\ \xi(z) = 0}.$$ The general theory of ordinary differential equations shows that, for every connected open $U \subseteq \RR^2 \setminus Z(\xi)$ and every $z \in U$, there exists…