Bifurcation of tetration below E^-E

[andydude]

A complete analysis of such questions considering also the complex
roots involves the T function as shown by Hayes in ND Hayes "The roots of the equation \( x = c \exp^n(x) \) and the cycles of the substitution \( x \rightarrow ce^x \)

I think the tree function is T(x) = -W(-x).

I like T because it allows H to be defined \( h(x) = \frac{T(\ln x)}{\ln x} \) very simply.

Andrew Robbins