Lyapunov Orbits in the $n$-Vortex Problem

    2014, Volume 19, Number 3, pp.  348-362

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

    In the reduced phase space by rotation, we prove the existence of periodic orbits of the $n$-vortex problem emanating from a relative equilibrium formed by $n$ unit vortices at the vertices of a regular polygon, both in the plane and at a fixed latitude when the ideal fluid moves on the surface of a sphere. In the case of a plane we also prove the existence of such periodic orbits in the $(n+1)$-vortex problem, where an additional central vortex of intensity κ is added to the ring of the polygonal configuration.
    Keywords: point vortices, relative equilibria, periodic orbits, Lyapunov center theorem
    Citation: Carvalho A. C., Cabral H. E., Lyapunov Orbits in the $n$-Vortex Problem, Regular and Chaotic Dynamics, 2014, Volume 19, Number 3, pp. 348-362

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