A parabolic Pommerenke-Levin-Yoccoz inequality

Xavier Buff, and Adam L. Epstein. "A parabolic Pommerenke-Levin-Yoccoz inequality." Fundamenta Mathematicae 172.3 (2002): 249-289. <http://eudml.org/doc/283244>.

@article{XavierBuff2002,
abstract = { 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. },
author = {Xavier Buff, Adam L. Epstein},
journal = {Fundamenta Mathematicae},
keywords = {holomorphic dynamics; parabolic; holomorphic index; Pommerenke-Levin-Yoccoz inequality},
language = {eng},
number = {3},
pages = {249-289},
title = {A parabolic Pommerenke-Levin-Yoccoz inequality},
url = {http://eudml.org/doc/283244},
volume = {172},
year = {2002},
}

TY - JOUR
AU - Xavier Buff
AU - Adam L. Epstein
TI - A parabolic Pommerenke-Levin-Yoccoz inequality
JO - Fundamenta Mathematicae
PY - 2002
VL - 172
IS - 3
SP - 249
EP - 289
AB - 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.
LA - eng
KW - holomorphic dynamics; parabolic; holomorphic index; Pommerenke-Levin-Yoccoz inequality
UR - http://eudml.org/doc/283244
ER -