  We study, through a new perspective, a globally coupled map system that
essentially interpolates between simple discrete-time nonlinear dynamics and
certain long-range many-body Hamiltonian models. In particular, we exhibit
relevant similarities, namely (i) the existence of long-standing
quasistationary states (QSS), and (ii) the emergence of weak chaos in the
thermodynamic limit, between the present model and the Hamiltonian Mean Field
model, a strong candidate for a nonxtensive statistical mechanical approach.
