  By the linearization property of Lipschitz-free spaces, any Lipschitz map $f
: M \to N$ between two pointed metric spaces may be extended uniquely to a
bounded linear operator $\widehat{f} : \mathcal F(M) \to \mathcal F(N)$ between
their corresponding Lipschitz-free spaces. In this note, we explore the
connections between the dynamics of Lipschitz self-maps $f : M \to M$ and the
linear dynamics of their extensions $\widehat{f} : \mathcal F(M) \to \mathcal
F(M)$. This not only allows us to relate topological dynamical systems to
linear dynamical systems but also provide a new class of hypercyclic operators
acting on Lipschitz-free spaces.
