Deformation of geometry and bifurcations of vortex rings

James Montaldi, Tadashi Tokieda

    Research output: Working paper

    107 Downloads (Pure)


    We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces, parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a necessary tool.
    Original languageEnglish
    Place of PublicationUniversity of Manchester
    Number of pages26
    Publication statusPublished - Apr 2012

    Publication series

    NameMIMS Eprints
    PublisherManchester Institute for Mathematical Sciences School of Mathematics


    • vortices, curvature, symmetric bifurcations


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