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Title: Point vortices on the hyperboloid
Author: Nava Gaxiola, Citlalitl
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2013
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In Hamiltonian systems with symmetry, many previous studies have centred their attention on compact symmetry groups, but relatively little is known about the effects of noncompact groups. This thesis investigates the properties of the system of N point vortices on the hyperbolic plane H2, which has noncompact symmetry SL (2, R).The Poisson Hamiltonian structure of this dynamical system is presented and the relative equilibria conditions are found. We also describe the trajectories of relative equilibria with momentum value not equal to zero. Finally, stability criteria are found for a number of cases, focusing on N = 2, 3. These results are placed in context with the study of point vortices on the sphere, which has compact symmetry.
Supervisor: Montaldi, James Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: point vortices ; hyperboloid ; relative equilibria ; stability of relative equilibria