Iterated polynomials

[Gottfried]

I've seen some of you talking about half-iterates of the sin function and I can only guess this is from a general formulae about partial iterates of polynomial functions. I was wondering if anyone had a link to anywhere explaining how to take the half iterate of any polynomial? I've tried searching all over google but I'm not having any luck. Any help would be greatly appreciated. Thank you.

Hm, perhaps -if not too elementary- you could look at
http://go.helms-net.de/math/tetdocs/Cont...ration.pdf

or

http://go.helms-net.de/math/tetdocs/FracIterAltGeom.htm

and some similar treatizes at my webspace. Also we had some discussions / elaborations (??? what a word) here on polynomial iterations.
But perhaps your question is a bit more specific?

And ehm, ps:another "perhaps" - you might reconsider to provide a name because I'd like it more in forums like this to be able to adress msgs more personally.

Gottfried