11/07/2009, 08:12 PM

(11/07/2009, 05:11 PM)bo198214 Wrote: But now there is still the question why the limit indeed satisfies

?

Actually it is not the case but we can obtain something very similar.

I just read in [1], p. 31, th. 10, that we have the following limit for a function

with :

for .

If we invert the formula we get

In our case though we dont have f(0)=0 but there is some fixed point of , .

In this case however the formula is quite similar, the only change is that .

[1] Ecalle: Theorie des invariants holomorphes