Repelling periodic point ($|(R^n)\prime (p)|>1$)

A holomorphic periodic point is repelling when its return multiplier has modulus greater than one. It belongs to the Julia set: if the iterates were normal near it, a subsequence of the return iterates, all fixing the point, would converge locally uniformly in the spherical metric. Near their fixed finite value the limit lies in a finite coordinate chart, so Cauchy's derivative estimate would bound their derivatives at the point. Those derivatives are the successive powers of the multiplier and are unbounded. The same argument in a reciprocal coordinate handles infinity.