Bifurcation of tetration below E^-E

[GFR]

1) For domain x<e^-e can odd and even h(x) be looked upon as separate continuous or infinitely differentiable functions?

2) Would the same apply to superroots in their oscillating domain?

My guessing is that what you called h-even and h-odd (the lower and upper limit of the "off limit" area) are the lower and upper branch of the same two-valued "function". The application of this idea to the superroots would imply the inversion of that "function", giving, this time arespectable one-valued function

To investigate that, I think it would be necessary to use all (so to say) the real and complex branches of the Lambert "function".

But this is my guessing!

GFR