© 2014 AIP Publishing LLC.We investigate the dynamical system of point vortices on the hyperboloid. This system has non-compact symmetry SL(2, R) and a coadjoint equivariant momentum map. 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 2 and 3 vortices. Unlike the system on the sphere, this system has relative equilibria with non-compact momentum isotropy subgroup, and these are used to illustrate the different stability types of relative equilibria.
- vortices, hamiltonian system with symmetry, stability, relative equilibria