# 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.

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