Porosity of Collet-Eckmann Julia sets

Abstract

We prove that the Julia set of a rational map of the Riemann sphere satisfying the Collet-Eckmann condition and having no parabolic periodic point is mean porous, if it is not the whole sphere. It follows that the Minkowski dimension of the Julia set is less than 2.

References in corpus (1)

• On measure and Hausdorff dimension of Julia sets for holomorphic Collet--Eckmann maps

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