  In search for mathematically tractable models of anomalous diffusion, we
introduce a simple dynamical system consisting of a chain of coupled maps of
the interval whose Lyapunov exponents vanish everywhere. The volume preserving
property and the vanishing Lyapunov exponents are intended to mimic the
dynamics of polygonal billiards, which are known to give rise to anomalous
diffusion, but which are too complicated to be analyzed as thoroughly as
desired. Depending on the value taken by a single parameter \alpha, our map
experiences sub-diffusion, super-diffusion or normal diffusion. Therefore its
transport properties can be compared with those of given L\'evy walks
describing transport in quenched disordered media. Fixing \alpha\ so that the
mean square displacement generated by our map and that generated by the
corresponding L\'evy walk asymptotically coincide, we prove that all moments of
the corresponding asymptotic distributions coincide as well, hence all
observables which are expressed in terms of the moments coincide.
