2014.40: Point vortices on the hyperbolic plane
2014.40: James Montaldi and Citlalitl Nava-Gaxiola (2014) Point vortices on the hyperbolic plane. J. Mathematical Physics, 55 (102702). pp. 1-14.
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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.
|Subjects:||MSC 2000 > 37 Dynamical systems and ergodic theory|
MSC 2000 > 70 Mechanics of particles and systems
|Deposited By:||Dr James Montaldi|
|Deposited On:||01 August 2014|