Lebesgue measure of Feigenbaum Julia sets

DOI10.4007/annals.2022.195.1.1zbMath1494.37026arXiv1504.02986OpenAlexW4206137692WikidataQ120786168 ScholiaQ120786168MaRDI QIDQ2078801

Artur Avila, Mikhail Lyubich

Publication date: 4 March 2022

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.02986

zbMATH Keywords

Julia setrenormalizationLebesgue measureFeigenbaum mapquadratic-like mapbounded combinatorics

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Renormalization of holomorphic dynamical systems (37F25) Combinatorics and topology in relation with holomorphic dynamical systems (37F20)

Related Items (7)

A transcendental Julia set of dimension 1 ⋮ The dynamics of complex box mappings ⋮ Lower bounds on the Hausdorff dimension of some Julia sets ⋮ A new perspective on the Sullivan dictionary via Assouad type dimensions and spectra ⋮ Local connectivity of the Mandelbrot set at some satellite parameters of bounded type ⋮ Convexity of complements of limit sets for holomorphic foliations on surfaces ⋮ On hyperbolic dimension gap for entire functions

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