09/09/2007, 08:37 AM

andydude Wrote:since you're talking about the series themselves, not finding them through matrices.

Yes, Koenigs method is an approximation method for the function outside the fixed point. He does not develop the coefficients of the iterated function (I think).

However that iterative roots are unique (in the real hyperbolic case) for formal power series must have been common knowledge for a quite long time, as it is easy to derive a recursive formula from the Faá di Bruno formula (without knowing about the matrix correspondence). And the steps from roots to fractional to continuous iteration are little ones.