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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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DOI: 10.1063/1.4897210

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 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 70 Mechanics of particles and systems
MIMS number:2014.40
Deposited By:Dr James Montaldi
Deposited On:01 August 2014

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