UNSPECIFIED (2002) A parabolic Pommerenke-Levin-Yoccoz inequality. FUNDAMENTA MATHEMATICAE, 172 (3). pp. 249-289. ISSN 0016-2736

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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 : P-1 --> P1, the number N of attracting petals and the residue l(f,beta) of the 1-form dz/(z - f (z)) at beta. 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

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	FUNDAMENTA MATHEMATICAE
Publisher:	POLISH ACAD SCIENCES INST MATHEMATICS
ISSN:	0016-2736
Date:	2002
Volume:	172
Number:	3
Number of Pages:	41
Page Range:	pp. 249-289
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/10421

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