Ensembles de Julia quadratiques de mesure de Lebesgue strictement positive

In this Note, we prove a variant of a conjecture stated in the thesis of Chéritat. The proof is based on results announced by Inou and Shishikura, and on earlier results of McMullen and of Chéritat. According to Chéritat's thesis, this allows us to complete a plan initiated by Douady and to show that there exist quadratic polynomials having a Julia set of positive Lebesgue measure. To cite this article: X. Buff, A. Chéritat, C. R. Acad. Sci. Paris, Ser. I 341 (2005).