2 real fixpoints again .......

[sheldonison]

\( f(x)=x^2+\sum_{n=3}^{\infty}a_n\cdot x^n\; \) ... one from the superattracting fixed point ...One could look at Miller's book for the general form for putting the super-attracting fixed point function in congruence with the unit circle.

The " helping function " from the OP was x^2.
Notice it is hard or even impossible to get a new helping function from An old one

Tommy, the super-attracting fixed point at zero is actually an easy problem. You can get the Abel function from the formal Böttcher's function for the super-attracting fixed point. Among my pari-gp scripts, are solutions for the Böttcher function and its inverse for any arbitrary super-attracting fixed point series, and the corresponding Abel function and Superfunction for that arbitrary f(z) series: \( f(z)=z^2+\sum_{n=3}^{\infty}a_n\cdot z^n \)
\( B(f(z)) = B(z)^2\;\; \) definintion of the Böttcher function for f(z)
\( \alpha(z) = \ln_2(-ln_2(B(z)))\;\; \) the Abel function for f(z)