Point vortices on the hyperboloid

Nava Gaxiola, Citlalitl (2013) Point vortices on the hyperboloid. Doctoral thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.

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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 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 relative equilibria conditions are found. We also describe the trajectories of equilibria with momentum value not equal to zero. Finally, stability criteria are found for a number of cases, focusing on N = 2 and 3. These results are placed in with the study of point vortices on the sphere, which has compact symmetry.

Item Type: Thesis (Doctoral)
Uncontrolled Keywords: Non-compact symmetry, point vortices, stability, relative equilibria
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: 09 Oct 2013
Last Modified: 20 Oct 2017 14:13
URI: https://eprints.maths.manchester.ac.uk/id/eprint/2022

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