levy ecalle koenigs ?

[sheldonison]

.....in fact i would like to see a limit like superfunction type of solution to parabolic iteration , something similar to koenigs non-parabolic iteration solution.

does there exist a method for all fixpoints ( parabolic or non-parabolic ) in terms of a limit , not using carleman ?

\( \eta=e^{1/e} \) is parabolic. Khoustenov gives the equation for the assymptotic behavior, although convergence is slow.
http://en.citizendium.org/wiki/Tetration
> At b=e^(1/e) , the limiting value L=e, and, asymptotically,
> F(z)=e - 2e/z + error term