  Following the general results on the relationships about Backlund
transformations (BTs) and exact discretisation given in a previous work [12],
we consider the Ablowitz-Ladik hierarchy and a corresponding family of BTs.
After discussing the boundary conditions, we show how to get explicit
transformations. The Hamiltonian properties of the maps and of the discrete
flows are examined. The conditions on the parameters of the map giving exact
discretisations are discussed. Finally, analytical and numerical examples are
given.
