Point vortices on the hyperbolic plane
Dynamical Systems
2014-11-17 v2
Abstract
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.
Cite
@article{arxiv.1403.2138,
title = {Point vortices on the hyperbolic plane},
author = {Citlalitl Nava-Gaxiola and James Montaldi},
journal= {arXiv preprint arXiv:1403.2138},
year = {2014}
}
Comments
To appear in J. Mathematical Physics