On extension to "other" iteration roots

[JmsNxn]

1. if you're taking the lower bases, there'll be 2 fixed point,

Yes outside of shell thron \(\eta^- - \delta\) you get a pair of fixed points.

Which two fixed points are you talking about? If the base moves through \(\eta_-\) there is no fixed point split or something.
There is *one* real fixed point, if the base is left of \(\eta_-\) or right of \(\eta_-\) (b<1).
AFAIK there are only two cases when a fixed point comes into existence or vanishes:
1. at \(b=\eta\) two real fixed points merge into 1 fixed point and then already split into two again
2. at \(b=1\) the right real fixed vanishes to infinity (coming from eta) 
I mean there are two additional complex conjugated fixed points a bit to the left for b at eta minor, but these fixed points are continuous in b, a small vicinity around eta minor maps to a small vicinity around these fixed points. So nothing coming into existence below eta minor.
In this post is an overview of the complex fixed points on the STB.

Or is Leo talking about the *additional* fixed points of b^b^x?
Like shown in this post? Which has to do with the construction of the P method that makes a merge of the even and odd iterates.

Well I can clarify, that I meant if I didn't make my typo. We can write a super function:

\[
F(t) = \Psi^{-1}(\cos(\pi t) |s|^t \Psi(z_0))\\
\]

When \(b = \eta^- + \delta\). And what I presumed Leo meant, is that for \(\eta^- - \delta\) (which I stupidly wrote), implies that the nearest fixed points are the conjugate pairs (which are still there for \(b = \eta^- + \delta\), but aren't the "primary fixed point/points"). But once you go outside of the shell thron region, you get (when forcing real valued solutions) two complex conjugate fixed points. That's what I interpreted from Leo's comment. Perhaps I read him wrong.

My original comment was poisoned by a typo, lmao, I should've just written \(b = \eta^- + \delta\), and this whole situation would've been avoided. Hope I'm not being obtuse or anything, lol.

Let's say, nearest fixed point to the real line; and that \(b = \eta^- + \delta\) has a real fixed point. And \(b = \eta^- - \delta\) has conjugate fixed point pairs as the closest.