Fibonacci as iteration of fractional linear function

[Leo.W]

And the fixed point's multiplier were positive, not negative as ours.

It is negative, that's what I mean with similar to our case.
\(f(x)=b^x\), \(b=\eta_-=e^{-e}\), parabolic fixed point \(z_0=\frac{1}{e}\), \(f'(x)=\log(b)b^x\), \(f'(z_0)=\log(b)z_0=-e\frac{1}{e}=-1\).

Oh I see u meant eta minor as \(e^{-e}\) I thought it was \(e^{\frac{1}{e}}_-\)
btw negative ones can be generated easily, here's another https://math.eretrandre.org/tetrationfor...p?tid=1351
I built about tetration base 0.5, at fixed point 0.707.
Albeit these superfunctions would oscillate around the fixed point as a limit at infty, thus uninvertible, and thus would not grant you for \(f^s\circ f^t=f^{s+t}\), they're contradicts.