properties of abel functions in general

[bo198214]

Let us summarize what are known about superfunctions, abel functions, etc.

*Let f be a holo. function. Let A be an abel function of f. if a is a fixed point of f, then A has a logarithmic branch point at A. not necessarily a log branch pt. but still some kind of singularity.

If you consider regular iteration at a hyperbolic fixed point \( z_0 \), then definitely the Abel function has a logarithmic singularity there. It is of the form:
\( \log_c(z-z_0)+p(z) \) where \( c=f'(z_0) \) and \( p \) is some analytic function in the vicinity of \( z_0 \).