For three equal masses in any number of dimensions (this might not be important, but 2D or 3D or 4D is fine) under just classical gravity (i.e., inverse-square force law), what stable periodic orbits are currently known?

The only solution I am aware of is the "figure-8" on Wikipedia, but surely there are more.

I think the biggest challenge here is stability. I try to define it below, but your definition is probably acceptable also. Anyway, I see hundreds of orbits posted on the internet, but I wonder if most of these degrade to chaos after continued simulation.

## Stability:

You provide a candidate $t$-parametrized "periodic limit orbit" $O$ (i.e., the functions $r(t)$ and $v(t)$) from which you choose any "generating point" $G$ (i.e., a specific $t_0$ prescribing $r(t_0)$ and $v(t_0)$).

Define the "epsilon-radius tube" about $O$ naturally. Define the "delta-radius ball" about $G$ a little more carefully by constraining points in this ball to not change the center of mass (otherwise, center of mass "drift" prevents any orbit from being stable).

Then, for every small epsilon I give, if you can provide a sufficiently-small delta such that the generated path stays within "a unitary transformation of the tube" forever, your candidate is stable.

EDIT: I changed from "the tube" to "a unitary transformation of the tube" to allow for a broader "rotating stability" (otherwise, rotation "drift" prevents any orbit from being stable). I believe this then covers all conservation laws. Also, I believe the 21 equal-mass families discovered here (and the 23 unequal-mass families discovered here) do meet my stability criteria.