Quadratic Julia Sets with Positive Area

2006/05/18 by Xavier Buff, Buff, Xavier, Arnaud Chéritat +1 · 4 citations
Mathematics · #37FXX #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.math/0605514

openalex publication_date 2006/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of quadratic polynomials having a Julia set with positive Lebesgue measure in three cases: the presence of a Cremer fixed point, the presence of a Siegel disk, the presence of infinitely many (satellite) renormalizations.

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