Periodic boundary points for simply connected Fatou components of transcendental maps

2024/04/17 by Anna Jové, Jové, Anna · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2404.11094

openalex publication_date 2024/04/17 · openalex created_date 2024/04/19 · openalex updated_date 2026/07/28

Abstract

Let f be a transcendental map, and let U be an attracting or parabolic basin, or a doubly parabolic Baker domain. Assume U is simply connected. Then, we prove that periodic points are dense in the boundary of U, under certain hypothesis on the postsingular set. This generalizes a result by F. Przytycki and A. Zdunik for rational maps. Our proof uses techniques from measure theory, ergodic theory, conformal analysis, and inner functions. In particular, a result on the distortion of inner functions near the unit circle is provided, which is of independent interest.

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• Boundaries of multiply connected Fatou components. A unified approach

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