2004/07/05 by Artur Avila, Avila, Artur, Mikhail Lyubich +1
Mathematics · #37F25 #37F45 #Advanced Topology and Set Theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #math.CV #math.DS #msc:37F25 #msc:37F45
paper · pdf · doi:10.48550/arxiv.math/0407066
13 pages
arxiv created 2004/07/05 · openalex publication_date 2004/07/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give examples of infinitely renormalizable quadratic polynomials Fc: z\maps to z2+c with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrar y close to 1. The combinatorics of the renormalization involved is close to the Chebyshev one . The argument is based upon a new tool, a ``Recursive Quadratic Estimate'' for the Poincaré series of an infinitely re normalizable map.