Quadratic Julia sets with positive area

Abstract

We prove the existence of quadratic polynomials having a Julia set with positive Lebesgue measure. We find such examples with a Cremer fixed point, with a Siegel disk, or with infinitely many satellite renormalizations.

Authors

Xavier Buff

Université de Toulouse
Institut de Mathématiques de Toulouse
118, route de Narbonne
31062 Toulouse
France

Arnaud Chéritat

Université de Toulouse
Institut de Mathématiques de Toulouse
118, route de Narbonne
31062 Toulouse
France