Point vortices on the sphere: Stability of symmetric relative equilibria

Frederic Laurent-Polz, James Montaldi, Mark Roberts

    Research output: Contribution to journalArticlepeer-review

    88 Downloads (Pure)


    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. © American Institute of Mathematical Sciences.
    Original languageEnglish
    Pages (from-to)439-486
    Number of pages47
    JournalJournal of Geometric Mechanics
    Issue number4
    Publication statusPublished - Dec 2011


    • Bifurcations
    • Hamiltonian systems
    • Point vortices
    • Stability
    • Symmetry


    Dive into the research topics of 'Point vortices on the sphere: Stability of symmetric relative equilibria'. Together they form a unique fingerprint.

    Cite this