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2006.246: Relative equilibria of point vortices on the sphere

2006.246: Chjan Lim, James Montaldi and Mark Roberts (2001) Relative equilibria of point vortices on the sphere. Physica D: Nonlinear Phenomena, 148. pp. 97-135. ISSN 0167-2789

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DOI: 10.1016/S0167-2789(00)00167-6


We prove the existence of many different symmetry types of relative equilibria for systems of identical point vortices on a non-rotating sphere. The proofs use the rotational symmetry group SO(3) and the resulting conservation laws, the time-reversing reflectional symmetries in O(3), and the finite symmetry group of permutations of identical vortices. Results include both global existence theorems and local results on bifurcations from equilibria. A more detailed study is made of relative equilibria which consist of two parallel rings with n vortices in each rotating about a common axis. The paper ends with discussions of the bifurcation diagrams for systems of 3–6 identical vortices.

Item Type:Article
Uncontrolled Keywords:Point vortices; Symmetry; First integrals; Flow on a sphere
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 70 Mechanics of particles and systems
MIMS number:2006.246
Deposited By:Ms Lucy van Russelt
Deposited On:08 August 2006

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