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2005.28: Point Vortices on the Sphere: Stability of Symmetric Relative Equilibria

2005.28: Frederic Laurent-Polz, James Montaldi and Mark Roberts (2011) Point Vortices on the Sphere: Stability of Symmetric Relative Equilibria. Journal of Geometric Mechanics, 3 (4). pp. 439-486. ISSN 1941-4897

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DOI: 10.3934/jgm.2011.3.439


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.

Item Type:Article
Uncontrolled Keywords:Hamiltonian systems, symmetry methods, bifurcations, momentum map, point vortices
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 76 Fluid mechanics
MIMS number:2005.28
Deposited By:Dr James Montaldi
Deposited On:29 March 2011

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