All bounded type Siegel disks of rational maps are quasi-disks

2008/10/15 by Gaofei Zhang, Zhang, Gaofei
Mathematics · #37F10 #37F20 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0810.2733

openalex publication_date 2008/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every bounded type Siegel disk of a rational map must be a quasi-disk with at least one critical point on its boundary. This verifies Douady-Sullivan conjecture for bounded type Siegel disks.

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