  For a proper, Gromov-hyperbolic metric space and a discrete, non-elementary,
group of isometries, we define a natural subset of the limit set at infinity of
the group called the ergodic limit set. The name is motivated by the fact that
every ergodic measure which is invariant for the geodesic flow on the quotient
metric space is concentrated on geodesics with endpoints belonging to the
ergodic limit set. We refine the classical Bishop-Jones' Theorem proving that
the packing dimension of the ergodic limit set coincides with the critical
exponent of the group.
