Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidly rotating, incompressible spheroid-ring systems: new
  bifurcations, critical rotations and degenerate states   The equilibrium of incompressible spheroid-ring systems in rigid rotation is
investigated by numerical means for a unity density contrast. A great diversity
of binary configurations is obtained, with no limit neither in the mass ratio,
nor in the orbital separation. We found only detached binaries, meaning that
the end-point of the $\epsilon_2$-sequence is the single binary state in strict
contact, easily prone to mass-exchange. The solutions show a remarkable
confinement in the rotation frequency-angular momentum diagram, with a total
absence of equilibrium for $\Omega^2/ \pi G \rho \gtrsim 0.21$. A short band of
degeneracy is present next to the one-ring sequence. We unveil a continuum of
bifurcations all along the ascending side of the Maclaurin sequence for
eccentricities of the ellipsoid less than $\approx 0.612$ and which involves a
gradually expanding, initially massless loop.

26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio