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

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## Abstract

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 |
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Uncontrolled Keywords: | Point vortices; Symmetry; First integrals; Flow on a sphere |

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: | Ms Lucy van Russelt |

Date Deposited: | 08 Aug 2006 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/447 |

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