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Lebesgue measure of Feigenbaum Julia sets

2015/04/12 by Artur Avila, Avila, Artur, Mikhail Lyubich +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1504.02986

arxiv created 2015/04/19 · arxiv updated 2015/04/21

Abstract

We construct Feigenbaum quadratic polynomials whose Julia sets have positive Lebesgue measure. They provide first examples of rational maps for which the hyperbolic dimension is different from the Hausdorff dimension of the Julia set. The corresponding set of parameters has positive Hausdorff dimension.

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