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 properties of abel functions in general bo198214 Administrator Posts: 1,395 Threads: 91 Joined: Aug 2007 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 $z_0$, 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 $z_0$. « Next Oldest | Next Newest »

 Messages In This Thread properties of abel functions in general - by Base-Acid Tetration - 10/24/2009, 12:28 AM RE: properties of abel functions in general - by andydude - 10/24/2009, 12:45 AM RE: properties of abel functions in general - by Base-Acid Tetration - 10/24/2009, 02:15 AM RE: properties of abel functions in general - by bo198214 - 10/24/2009, 10:10 AM

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