Fibonacci as iteration of fractional linear function

[bo198214]

Oh I see u meant eta minor as \(e^{-e}\) I thought it was \(e^{\frac{1}{e}}_-\)

That's eta proper (or maybe eta major) \(\eta=e^{\frac{1}{e}}\) - that's how we call it on this forum

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.

Well, I think I need a while to digest all your suggestions ...

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.

Well, then its not a superfunction, isn't it?! Just don't know whether James superfunction is a real superfunction ... this oscillating behaviour looked very similar to James function.