Suppose p is a repelling ﬁxed point of a map f . Then there is some nbhd Nϵ (p) so that for any x not equal to p and x ∈ Nϵ (p), there is some n* so that that for all n ≥ n*, f^{n}(x) not in Nϵ(p).

Let d = ϵ. If k = n* we have

|f^{k}(x) -f^{k}(p)| = |f^{k}(x) -(p)| = >= ϵ = d

therefore has sensitive dependence.