07/09/2010, 05:46 AM

(07/08/2010, 11:31 PM)tommy1729 Wrote: for parabolic iteration i use the carleman matrix method.

What you mean by carleman method?

We have Andrews intuitive Abel function which uses the Carleman matrix as well as Gottfrieds matrix power method.

Also I dont know how you do that if you develop at a fixed point, or dont you? Matrix power method at a fixed point is equal to regular/parabolic iteration and yields a series expansion that has convergence radius 0.

Quote:what other methods exist ?

bo mentioned " levy and ecalle " but i dont know about their parabolic iteration formula's ...

...

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.

Its explained in my overview paper (see the FAQ thread).

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

something like that.

Quote:im sorry , i tried looking on the internet , but found nothing apart from stuff that is equivalent to carleman ...

look at my overview paper, everything is explained there though its quite raw yet. If you have specific question you can always ask me.

Quote:if i recall correct , koenigs is not necc analytic. are there similar methods that only work when the solution is analytic ?

koenigs is analytic (in vicinity of the hyperbolic fixed point, though some authors also call the Levy formula for parabolic fixed point "koenigs").