10/24/2009, 10:10 AM

(10/24/2009, 12:28 AM)Base-Acid Tetration Wrote: 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 , then definitely the Abel function has a logarithmic singularity there. It is of the form:

where and is some analytic function in the vicinity of .