= Superattracting periodic point
{title2=$(R^n)\prime(p)=0$}
A holomorphic periodic point is superattracting if its return multiplier is zero. The return map then has local expansion $G(p+u)=p+a u^e+O(u^{e+1})$ with $e\geq2$. This implies a strict contraction on a sufficiently small disc and rapid convergence of returns. Infinity is superattracting for every polynomial of degree at least two: the reciprocal-coordinate return has a zero of order equal to the polynomial degree.
Back to article page
