2001/05/27 by Artur Avila, A. Avila, Avila, Artur +2
Mathematics · #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #math.DS
paper · pdf · doi:10.48550/arxiv.math/0105222
34 pages, no figures, first version
arxiv created 2001/05/27 · openalex publication_date 2001/05/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider quasisymmetric reparametrizations of the parameter space of the quadratic family. We prove that the set of quadratic maps which are either regular or Collet-Eckmann with polynomial recurrence of the critical orbit has full Lebesgue measure. (The intent of this work is just to be a rigorous reference for the companion preprint Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative. It is based on the LaTeX file of the paper Statistical properties of unimodal maps: the quadratic family. The proofs are very similar and in many places differ just by change of constants.)