6 Se p 20 09 Rosette Central Configurations , Degenerate central configurations and bifurcations

In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian n-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where n particles of mass m1 lie at the vertices of a regular n-gon, n particles of mass m2 lie at the vertices of another n-gon concentric with the first, but rotated of an angle π/n, and an additional particle of mass m0 lies at the center of mass of the system. This system admits two mass parameters µ = m0/m1 and ǫ = m2/m1. We show that, as µ varies, if n > 3, there is a degenerate central configuration and a bifurcation for every ǫ > 0, while if n = 3 there is a bifurcations only for some values of ǫ.