Global bifurcation of polygonal relative equilibria for masses, vortices and dNLS oscillators

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.