  Consider a symplectic surface $\Sigma$ with two properly embedded Hamiltonian
isotopic curves $L$ and $L'$. Suppose $g \in Ham (\Sigma)$ is a Hamiltonian
diffeomorphism which sends $L$ to $L'$. Which dynamical properties of $g$ can
be detected by the pair $(L, L')$? We discuss two cases where one can deduce
that $g$ is `chaotic': non-autonomous or even of positive entropy.
