UNSPECIFIED (2001) Relative equilibria of point vortices on the sphere. PHYSICA D-NONLINEAR PHENOMENA, 148 (1-2). 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. (C) 2001 Elsevier Science B.V. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	PHYSICA D-NONLINEAR PHENOMENA
Publisher:	ELSEVIER SCIENCE BV
ISSN:	0167-2789
Date:	1 January 2001
Volume:	148
Number:	1-2
Number of Pages:	39
Page Range:	pp. 97-135
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/12554

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