Montaldi, James and Nava-Gaxiola, Citlalitl (2014) Point vortices on the hyperbolic plane. J. Mathematical Physics, 55 (102702). pp. 1-14. (In Press)
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Abstract
We investigate the dynamical system of point vortices on the hyperboloid. This system has noncompact 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 systemon 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.
| Item Type: | Article |
|---|---|
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems |
| Depositing User: | Dr James Montaldi |
| Date Deposited: | 01 Aug 2014 |
| Last Modified: | 20 Oct 2017 14:13 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2164 |
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