Primitive tuning via quasiconformal surgery

2020/10/11 by Weixiao Shen, Yimin Wang, Shen, Weixiao +1 · 1 citation
Mathematics · #37F10 #37F25 #37F31 #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2010.05199

openalex publication_date 2020/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using quasiconformal surgery, we prove that any primitive, postcritically-finite hyperbolic polynomial can be tuned with an arbitrary generalized polynomial with non-escaping critical points, generalizing a result of Douady-Hubbard for quadratic polynomials to the case of higher degree polynomials. This solves affirmatively a conjecture by Inou and Kiwi on surjectivity of the renormalization operator on higher degree polynomials in one complex variable.

Citations

• Combinatorics and topology of straightening maps II: Discontinuity
• Holomorphic Removability of Julia Sets

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• Gluing polynomials along the circle

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