Global bifurcation of planar and spatial periodic solutions from the polygonal relative equilibria for the n-body problem

Given n point masses turning in a plane at a constant speed, this paper deals with the global bifurcation of periodic solutions for the masses in that plane and in space. As a special case, one has a complete study of n identical masses on a regular polygon and a central mass. The symmetries of the problem are used in order to find the irreducible representations, the linearization, and with the help of the orthogonal degree theory, all the symmetries of the bifurcating branches.