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arXiv · 2009.02788

Periodic Points and Smooth Rays

Carsten L. Petersen·Saeed Zakeri
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Abstract

Let $P: {\mathbb C} \to {\mathbb C}$ be a polynomial map with disconnected filled Julia set $K_P$ and let $z_0$ be a repelling or parabolic periodic point of $P$. We show that if the connected component of $K_P$ containing $z_0$ is non-degenerate, then $z_0$ is the landing point of at least one {\it smooth} external ray. The statement is optimal in the sense that all but one ray landing at $z_0$ may be broken.

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Carsten L. Petersen, Saeed Zakeri. 2020-09-06. Periodic Points and Smooth Rays. https://doi.org/10.1090/ecgd%2F364

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