  In reason of the strongly non-ergodic dynamical behavior, universality
properties of deterministic Fixed-Energy Sandpiles are still an open and
debated issue. We investigate the one-dimensional model, whose microscopical
dynamics can be solved exactly, and provide a deeper understanding of the
origin of the non-ergodicity. By means of exact arguments, we prove the
occurrence of orbits of well-defined periods and their dependence on the
conserved energy density. Further statistical estimates of the size of the
attraction's basins of the different periodic orbits lead to a complete
characterization of the activity vs. energy density phase diagram in the limit
of large system's size.
