Yes, it does. See the full statement of Theorem 2 on page 6. The assumptions of the theorem are:
Suppose that a rational map f0 of degree d(>1) has a parabolic fixed
point ζ with multiplier exp(2πip/q) (p,qinmathbbZ,mathitgcd(p,q)=1) and that the immediate parabolic basin of ζ contains only one critical point of f0.
This is the case for zd+c.
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