Positive measure Julia sets and Siegel disks of quadratic polynomials

Jean-Christophe Yoccoz

Séminaire Bourbaki (2005-2006)

  • Volume: 48, page 385-402
  • ISSN: 0303-1179

Abstract

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Xavier Buff and Arnaud Chéritat have shown that the Julia sets of some quadratic polynomials have positive Lebesgue measure, answering a question open since Fatou and Julia. These polynomials have an indifferent fixed point with carefully selected rotation number. We will explain the main steps of their proof and present related results of the same authors on the geometry and the size of Siegel disks.

How to cite

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Yoccoz, Jean-Christophe. "Ensembles de Julia de mesure positive et disques de Siegel des polynômes quadratiques." Séminaire Bourbaki 48 (2005-2006): 385-402. <http://eudml.org/doc/252151>.

@article{Yoccoz2005-2006,
abstract = {Xavier Buff et Arnaud Chéritat ont montré que l’ensemble de Julia de certains polynômes quadratiques est de mesure de Lebesgue positive, répondant ainsi à une question ouverte depuis Fatou et Julia. Les polynômes en question ont un point fixe indifférent irrationnel dont le nombre de rotation doit être soigneusement déterminé. On exposera les grandes lignes de la démonstration, ainsi que d’autres résultats connexes des mêmes auteurs sur la géométrie et la taille des disques de Siegel.},
author = {Yoccoz, Jean-Christophe},
journal = {Séminaire Bourbaki},
keywords = {Julia sets; Siegel disks; holomorphic dynamics},
language = {fre},
pages = {385-402},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {Ensembles de Julia de mesure positive et disques de Siegel des polynômes quadratiques},
url = {http://eudml.org/doc/252151},
volume = {48},
year = {2005-2006},
}

TY - JOUR
AU - Yoccoz, Jean-Christophe
TI - Ensembles de Julia de mesure positive et disques de Siegel des polynômes quadratiques
JO - Séminaire Bourbaki
PY - 2005-2006
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 48
SP - 385
EP - 402
AB - Xavier Buff et Arnaud Chéritat ont montré que l’ensemble de Julia de certains polynômes quadratiques est de mesure de Lebesgue positive, répondant ainsi à une question ouverte depuis Fatou et Julia. Les polynômes en question ont un point fixe indifférent irrationnel dont le nombre de rotation doit être soigneusement déterminé. On exposera les grandes lignes de la démonstration, ainsi que d’autres résultats connexes des mêmes auteurs sur la géométrie et la taille des disques de Siegel.
LA - fre
KW - Julia sets; Siegel disks; holomorphic dynamics
UR - http://eudml.org/doc/252151
ER -

References

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