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A parabolic Pommerenke-Levin-Yoccoz inequality

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Buff X., Epstein A.

Fundamenta Mathematicae

2002

tom 172

nr 3

249-289

In a recent preprint [B], Bergweiler relates the number of critical points contained in the immediate basin of a multiple fixed point β of a rational map f: ℙ¹ → ℙ¹, the number N of attracting petals and the residue ι(f,β) of the 1-form dz/(z-f(z)) at β. In this article, we present a different approach to the same problem, which we were developing independently at the same time. We apply our method to answer a question raised by Bergweiler. In particular, we prove that when there are only N grand orbit equivalence classes of critical points in the immediate basin, then ℜ((N+1)/2 - ι(f,β)) > N/π².

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1 Fundamenta Mathematicae

1 Buff X.

1 Epstein A.

1 2002

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A parabolic Pommerenke-Levin-Yoccoz inequality