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arXiv · 2404.11094

Periodic boundary points for simply connected Fatou components of transcendental maps

Anna Jové
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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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Anna Jové. 2024-04-17. Periodic boundary points for simply connected Fatou components of transcendental maps. https://arxiv.org/abs/2404.11094

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