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Point vortices on the sphere: stability of relative equilibria

Frédéric Laurent-Polz·James Montaldi·Mark Roberts
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Abstract

We describe the linear and nonlinear stability and instability of certain symmetric configurations of point vortices on the sphere forming relative equilibria. These configurations consist of one or two rings, and a ring with one or two polar vortices. Such configurations have dihedral symmetry, and the symmetry is used to block diagonalize the relevant matrices, to distinguish the subspaces on which their eigenvalues need to be calculated, and also to describe the bifurcations that occur as eigenvalues pass through zero.

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Frédéric Laurent-Polz, James Montaldi, Mark Roberts. 2004-02-26. Point vortices on the sphere: stability of relative equilibria. https://arxiv.org/abs/math/0402430

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