Lyapunov Orbits in the $n$-Vortex Problem on the Sphere

    2015, Volume 20, Number 3, pp.  234-246

    Author(s): Carvalho A. C., Cabral H. E.

    In the phase space reduced by rotation, we prove the existence of periodic orbits of the $(n + 1)$-vortex problem emanating from a relative equilibrium formed by $n$ unit vortices at the vertices of a regular polygon at a fixed latitude and an additional vortex of intensity κ at the north pole when the ideal fluid moves on the surface of a sphere.
    Keywords: point vortex problem, relative equilibria, periodic orbits, Lyapunov center theorem
    Citation: Carvalho A. C., Cabral H. E., Lyapunov Orbits in the $n$-Vortex Problem on the Sphere, Regular and Chaotic Dynamics, 2015, Volume 20, Number 3, pp. 234-246

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