Lebesgue measure of Feigenbaum Julia sets

Artur Avila; Mikhail Lyubich

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arXiv · 1504.02986

Lebesgue measure of Feigenbaum Julia sets

Artur Avila·Mikhail Lyubich

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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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Artur Avila, Mikhail Lyubich. 2015-04-19. Lebesgue measure of Feigenbaum Julia sets. https://arxiv.org/abs/1504.02986

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