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A parabolic Pommerenke-Levin-Yoccoz inequality
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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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | FUNDAMENTA MATHEMATICAE | ||||
Publisher: | POLISH ACAD SCIENCES INST MATHEMATICS | ||||
ISSN: | 0016-2736 | ||||
Official Date: | 2002 | ||||
Dates: |
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Volume: | 172 | ||||
Number: | 3 | ||||
Number of Pages: | 41 | ||||
Page Range: | pp. 249-289 | ||||
Publication Status: | Published |
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