Point vortices on the hyperbolic plane

James Montaldi, Citlalitl Nava-Gaxiola

    Research output: Contribution to journalArticlepeer-review


    © 2014 AIP Publishing LLC.We investigate the dynamical system of point vortices on the hyperboloid. This system has non-compact symmetry SL(2, R) and a coadjoint equivariant momentum map. The relative equilibrium conditions are found and the trajectories of relative equilibria with non-zero momentum value are described. We also provide the classification of relative equilibria and the stability criteria for a number of cases, focusing on 2 and 3 vortices. Unlike the system on the sphere, this system has relative equilibria with non-compact momentum isotropy subgroup, and these are used to illustrate the different stability types of relative equilibria.
    Original languageEnglish
    Article number102702
    Pages (from-to)1-14
    Number of pages13
    JournalJournal of Mathematical Physics
    Issue number10
    Publication statusPublished - 6 Oct 2014


    • vortices, hamiltonian system with symmetry, stability, relative equilibria


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