Bifurcation of tetration below E^-E

[Ivars]

I still want to be around

A quote from Corless: http://www.apmaths.uwo.ca/~rcorless/fram.../LambertW/
Robert M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, ``On the Lambert W Function", Advances in Computational Mathematics, volume 5, 1996, pp. 329--359.

Euler observed in L. Euler De formulis exponentialibus replicatis'
that the equation g= z^z^g sometimes has real roots g that are
not roots of h=z^h. 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 ce^x

Ivars