suppose I have a meromorphic iterated function f(x) with a removable singularity at its fixed point. The derivative exists and is < 1 at the fixed point, How would I find a continuous parameterization such that f(...f(f(x))...)=ng(x) where n is the multiplier to some power? The function doesn't seem to have a finite second derivative, none of the change of coordinates I've tried have worked. Is g(x) even possible to find?