  Given a regular polygonal arrangement of identical objects, turning around a
central object (masses, vortices or dNLS oscillators), this paper studies the
global bifurcation of relative equilibria in function of a natural parameter
(central mass, central circulation or amplitude of the oscillation). The
symmetries of the problem are used in order to find the irreducible
representations, the linearization and, with the help of a degree theory, the
symmetries of the bifurcated solutions.
