Uniformly rotating axisymmetric fluid configurations bifurcating from highly flattened Maclaurin spheroids

We present a thorough investigation of sequences of uniformly rotating, homogeneous axisymmetric Newtonian equilibrium configurations that bifurcate from highly flattened Maclaurin spheroids. Each one of these sequences possesses a mass-shedding limit. Starting at this point, the sequences proceed towards the Maclaurin sequence and beyond. The first sequence leads to the well-known Dyson rings, whereas the end-points of the higher sequences are characterized by the formation of a two-body system, either a core-ring system (for the second, the fourth, etc., sequence) or a two-ring system (for the third, the fifth, etc., sequence). Although the general qualitative picture drawn by Eriguchi and Hachisu in the 1980s has been confirmed, slight differences arise in the interpretation of the origin of the first two-ring sequence and in the general appearance of fluid bodies belonging to higher sequences.