Bifurcations and phase transitions of self-gravitating and uniformly rotating fluid

Bifurcations for the uniformly rotating and self-gravitating incompressible fluid are classified into two types. When one equilibrium sequence is not tangent (tangent) to the other equilibrium sequence at the bifurcation point in the angular momentum-angular velocity plane and when the symmetry of the equilibrium figure breaks (preserves), it is defined as a bifurcation of the first (second) order. It has been proved that the bifurcation from the Maclaurin spheroid to the ring(s) equilibrium is of the second order. It is suggested that the bifurcation is closely akin to a phase transition because the behaviour of the specific moment of inertia corresponds to that of the specific heat and because the symmetry breakdown or preservation is also a feature of the phase transition. The first (second) order bifurcation corresponds to the second (third) order phase transition. (author)