Non-analyticity of hairs of exponential maps

Weiwei Cui; Jiaxing Huang; Lingrui Wang

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arXiv · 2609.32703

Non-analyticity of hairs of exponential maps

Weiwei Cui·Jiaxing Huang·Lingrui Wang

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Abstract

Let $f_λ(z)=λe^z$, where $0<λ<1/e$. In 1984, Devaney and Krych showed that the Julia set consists of pairwise disjoint hairs. Viana further in 1988 proved that these hairs are $C^{\infty}$. In this paper we show that hairs are not analytic except for trivial ones. This solves a long-standing open question.

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Weiwei Cui, Jiaxing Huang, Lingrui Wang. 2026-09-26. Non-analyticity of hairs of exponential maps. https://arxiv.org/abs/2609.32703

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