b^b^x with base 0<b<e^-e have three real fixpoints

[Gottfried]

Triggered by a question in the math.stackexchange-forum I looked at real fixpoints of b^b^x and found that for the smallest b<e^-e have three real fixpoints (while b^x has only one).

See a short compilation in:
https://math.stackexchange.com/a/2494323/1714

I have not yet found a closed-form expression - for instance by the Lambert W as in the fixpoint-problem of the simple case b^x.

Gottfried