%0 Journal Article
%T Point vortices on the hyperbolic plane
%A Citlalitl Nava-Gaxiola
%A James Montaldi
%J Mathematics
%D 2014
%I arXiv
%R 10.1063/1.4897210
%X 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.
%U http://arxiv.org/abs/1403.2138v2