Editing Appendix/Ramblings/BordeauxSequences (section)

===Key Figures===

====Eriguchi &amp; Sugimoto (1981)====

<table border="1" cellpadding="5" align="center" width="75%">
<tr><td align="center" bgcolor="orange">
Fig. 1 extracted without modification from p. 1873 of [https://academic.oup.com/ptp/article/65/6/1870/1908070 Eriguchi &amp; Sugimoto (1981)]<p></p>
"''Another Equilibrium Sequence of Self-Gravitating and Rotating Incompressible Fluid''"<p></p>
Progress of Theoretical Physics, <p></p>
vol. 65, pp. 1870-1875 &copy; Progress of Theoretical Physics
</td></tr>
<tr>
  <td align="center">
[[File:EriguchiSugimoto81Fig1.png|center|600px|Figure 3 from Eriguchi &amp; Hachisu (1983)]]
  </td>
</tr>
<tr>
  <td align="left">
CAPTION (modified here): &nbsp;  The squared angular velocity is plotted against <math>~j^2</math> for a segment of the Maclaurin sequence (dashed curve), for the Dyson-Wong sequence (dotted curve), and for the new configurations reported in this 1981 paper by Eriguchi &amp; Sugimoto (solid curve).  The "&times;" mark denotes the neutral point on the Maclaurin sequence against the <math>~P_4(\eta)</math> perturbation.  The dotted curve is plotted by using the values which are read from the curve of Fig. 6 of [https://ui.adsabs.harvard.edu/abs/1974ApJ...190..675W/abstract Wong (1974)], so it may contain errors to some extent.

  </td>
</tr>
</table>


====Eriguchi &amp; Hachisu (1983)====

<table border="1" cellpadding="5" align="center" width="75%">
<tr><td align="center" bgcolor="orange">
Fig. 3 extracted without modification from p. 1134 of [https://ui.adsabs.harvard.edu/abs/1983PThPh..69.1131E/abstract Eriguchi &amp; Hachisu (1983)]<p></p>
"''Two Kinds of Axially Symmetric Equilibrium Sequences of Self-Gravitating and Rotating Incompressible Fluids:<br />Two-Ring Sequence and Core-Ring Sequence''"<p></p>
Progress of Theoretical Physics, <p></p>
vol. 69, pp. 1131-1136 &copy; Progress of Theoretical Physics
</td></tr>
<tr>
  <td align="center">
[[File:EriguchiHachisu83 Fig3.png|center|800px|Figure 3 from Eriguchi &amp; Hachisu (1983)]]
  </td>
</tr>
<tr>
  <td align="left">
CAPTION: &nbsp;The angular momentum-angular velocity relations.  Solid curves represent uniformly rotating equilibrium sequences.
<ul>
<li>MS: &nbsp; Maclaurin spheroid sequence</li>
<li>JE: &nbsp; Jacobi ellipsoid sequence</li>
<li>OR: &nbsp; one-ring sequence</li>
</ul>
The number and letter ''R'' or ''C'' attached to a curve denote mass ratio and two-ring or core-ring sequence, respectively.  If differential rotation is allowed, the equilibrium sequences may continue to exist as shown by the dashed curves.
  </td>
</tr>
</table>

====AKM (2003)====

<table border="1" cellpadding="5" align="center" width="75%">
<tr><td align="center" bgcolor="orange">
Fig. 2 extracted without modification from p. 517 of [https://ui.adsabs.harvard.edu/abs/2003MNRAS.339..515A/abstract Ansorg, Kleinw&auml;chter &amp; Meinel (2003)]<p></p>
"''Uniformly rotating axisymmetric fluid configurations bifurcating from highly flattened Maclaurin spheroids''"<p></p>
MNRAS, vol. 339, pp. 515-523 &copy; Royal Astronomical Society
</td></tr>
<tr>
  <td align="center">
[[File:AKM2003Fig2.png|center|800px|Figure 2 from Ansorg, Kleinw&auml;chter &amp; Meinel (2003)]]
  </td>
</tr>
<tr>
  <td align="left">
CAPTION: &nbsp; For the first five axisymmetric sequences, <math>~\omega_0^2</math> is plotted against the dimensionless squared angular momentum, <math>~j^2</math>, using the same normalizations as Eriguchi &amp; Hachisu (1983).  Dotted and dashed curves again refer to the Maclaurin sequence and the Dyson approximation respectively.  The full circles mark the bifurcation points on the Maclaurin sequence, and the open square the transition configuration of spheroidal to toroidal bodies on the Dyson ring sequence.
  </td>
</tr>
</table>

====Basillais &amp; Hur&eacute; (2019)====

<table border="1" cellpadding="5" align="center" width="75%">
<tr><td align="center" bgcolor="orange">
Fig. 4 extracted without modification from p. 4507 of [https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.4504B/abstract Basillais &amp; Hur&eacute; (2019)]<p></p>
"''Rigidly rotating, incompressible spheroid-ring systems: &nbsp; new bifurcations, critical rotations, and degenerate states''"<p></p>
MNRAS, vol. 487, pp. 4504-4509 &copy; Royal Astronomical Society
</td></tr>
<tr>
  <td align="center">
[[File:BH2019Fig4.png|center|400px|Figure 4 from Basillais &amp; Hur&eacute; (2019)]]
  </td>
</tr>
<tr>
  <td align="left">
CAPTION: &nbsp; The spheroid-ring solutions (''grey dots'') populate the <math>~\omega_0^2 - j^2</math> diagram in between the MLS, the high-&omega; limit, and the high-j limit.  The MLS, ORS, Jacobi sequence, Hamburger sequence, and &epsilon;<sub>2</sub>-sequence are also shown (''plain lines'').  Points labelled a to f (''cross'') correspond to equilibria shown in Figure 3; see also Table 1.  There is a band of degeneracy rightward to the ORS (''green dashed zone'').
  </td>
</tr>
</table>