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arXiv · 2002.00853

The topological dimension of radial Julia sets

David S. Lipham
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Abstract

We prove that the meandering set for $f_a(z)=e^z+a$ is homeomorphic to the space of irrational numbers whenever $a$ belongs to the Fatou set of $f_a$. This extends recent results by Vasiliki Evdoridou and Lasse Rempe. It implies that the radial Julia set of $f_a$ has topological dimension zero for all attracting and parabolic parameters, including all $a\in (-\infty,-1]$. Similar results are obtained for Fatou's function $f(z)=z+1+e^{-z}$.

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David S. Lipham. 2020-02-03. The topological dimension of radial Julia sets. https://doi.org/10.1007/s40315-022-00449-1

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