Point vortices on the hyperbolic plane

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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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: http://eprints.maths.manchester.ac.uk/id/eprint/2164

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