Suppose that p is a fixed point of the differentiable function J and If’ (p) I = 1. If there exists a neighbourhood of p that is contained in the stable set of p, then p is weakly attracting. If there exists a neighbourhood U of p such that for each point x in U except p there is a positive integer n such that In(x) is not in U, then p is weakly repelling. Find an example of a function of the complex numbers with a weakly attracting or a weakly repelling fixed point.
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