Bo, this is very helpful. It substantiates my understanding of the dynamics of "indifferent" or irrationally neutral fixed points. Since my general Taylor's series of iterated functions is based on the summation of geometrical series, it is only natural to use the modulus. As far as Siegal in tetration, Robert Devaney claimed that the exponential map couldn't have a Siegal disk because it is exponentiation is entire. I believe that irrationally neutral dynamical systems are where the "small divisor problem" is considered.
Daniel