  Let $\mathcal{A}$ be a real line arrangement and $\mathcal{D}(\mathcal{A})$
the module of $\mathcal{A}$--derivations. First, we give a dynamical
interpretation of $\mathcal{D}(\mathcal{A})$ as the set of polynomial vector
fields which posses $\mathcal{A}$ as invariant set. We characterize polynomial
vector fields having an infinite number of invariant lines. Then we prove that
the minimal degree of polynomial vector fields fixing only a finite set of
lines in $\mathcal{D}(\mathcal{A})$ is not determined by the combinatorics of
$\mathcal{A}$.

Dynamical Systems