  Different sets of metastable states can be reached in glassy systems below
some transition temperature depending on initial conditions and details of the
dynamics. This is investigated for the Sherrington-Kirkpatrick spin glass model
with long ranged interactions. In particular, the time dependent local field
distribution and energy are calculated for zero temperature. This is done for a
system quenched to zero temperature, slow cooling or simulated annealing, a
greedy algorithm and repeated tapping. Results are obtained from Monte-Carlo
simulations and a Master-Fokker-Planck approach. A comparison with replica
symmetry broken theory, evaluated in high orders, shows that the energies
obtained via dynamics are higher than the ground state energy of replica
theory. Tapping and simulated annealing yield on the other hand results which
are very close to the ground state energy. The local field distribution tends
to zero for small fields. This is in contrast to the Edwards flat measure
hypothesis. The distribution of energies obtained for different tapping
strengths does again not follow the canonical form proposed by Edwards.
