Abstract
We propose a method to determine relative periodic orbits in point vortex systems: it consists mainly of performing a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is applied to point vortex systems on a sphere and on the plane, but works for other surfaces with isotropy (cylinder, ellipsoid, …). The method also permits us to determine some relative equilibria and heteroclinic cycles connecting these relative equilibria.
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