Rigidity of bounded type cubic Siegel polynomials

2023/11/01 by Jonguk Yang, Runze Zhang, Yang, Jonguk +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2311.00431

openalex publication_date 2023/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if two non-renormalizable cubic Siegel polynomials with bounded type rotation numbers are combinatorially equivalent, then they are also conformally equivalent. As a consequence, we show that in the one-parameter slice of cubic Siegel polynomials considered by Zakeri [Za2], the locus of non-renormalizable maps is homeomorphic to a double-copy of a quadratic Siegel filled Julia set (minus the Siegel disk) glued along the Siegel boundary. This verifies the the conjecture of Blokh-Oversteegen-Ptacek-Timorin [BlOvPtTi] for bounded type rotation numbers.

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