  We investigate the dynamics of many-body long-range interacting systems,
taking the Hamiltonian Mean Field model as a case study. We show that an
abundance of regular trajectories, associated with invariant tori of the
single-particle dynamics, exists. The presence of such tori provides a
dynamical interpretation of the emergence of long-lasting out-of-equilibrium
regimes observed generically in long-range systems. This is alternative to a
previous statistical mechanics approach to such phenomena which was based on a
maximum entropy principle. Previously detected out-of-equilibrium phase
transitions are also reinterpreted within this framework.
