A parabolic Pommerenke–Levin–Yoccoz inequality

Abstract

In a recent preprint [B], Bergweiler relates the number of critical points contained in the immediate basin of a multiple fixed point $\beta $ of a rational map $f: {\mathbb P}^1\to {\mathbb P}^1$, the number ${N}$ of attracting petals and the residue $\i