  We investigate some properties of the dynamical system of point vortices on
the hyperboloid. This system has noncompact symmetry SL(2, R) and a coadjoint
equivariant momentum map J. The relative equilibrium conditions are found and
the trajectories of relative equilibria with non-zero momentum value are
described. We also provide the classification of relative equilibria and the
stability criteria for a number of cases, focusing on N=2, 3. Contrary to the
system on the sphere, relative equilibria with non-compact momentum isotropy
subgroup are found, and are used to illustrate the different stability types of
relative equilibria.
