Holomorphic Dynamics of Quadratic Polynomials: The Area of Julia Sets and Yoccoz Puzzles

Zenodo (CERN European Organization for Nuclear Research) 2026 Open access

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Authors: Zen Revista, 10 MFC
DOI: 10.5281/zenodo.18142916
Cited by: 0

Abstract

We establish a rigorous bound on the Lebesgue measure of Julia sets for infinitely renormalizable quadratic polynomials via the modulus decay of Yoccoz puzzle annuli. The analysis utilizes transfinite induction on the puzzle depth and quasi-conformal surgery techniques.

Fields of Study & Subjects

Mathematical Dynamics and Fractals Holomorphic and Operator Theory Mathematical functions and polynomials

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
4 January 2026