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

Combinatorics of line arrangements and dynamics of polynomial vector fields