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arXiv · 2007.07951

Speiser class Julia sets with dimension near one

Christopher J. Bishop·Simon Albrecht
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Abstract

For any $ \delta >0$ we construct an entire function $f$ with three singular values whose Julia set has Hausdorff dimension at most $1=\delta$. Stallard proved that the dimension must be strictly larger than 1 whenever $f$ has a bounded singular set, but no examples with finite singular set and dimension strictly less than 2 were previously known.

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Christopher J. Bishop, Simon Albrecht. 2020-07-15. Speiser class Julia sets with dimension near one. https://arxiv.org/abs/2007.07951

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