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PreprintarXiv licencearXiv

Non-analyticity of hairs of exponential maps

  • Weiwei Cui
  • Jiaxing Huang
  • Lingrui Wang
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Abstract

Let fλ(z)=λez, 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∞. 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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Cite

BibTeXRIS
BibTeX
@misc{cui2026nonanalyticity,
  title = {{Non-analyticity of hairs of exponential maps}},
  author = {Weiwei Cui and Jiaxing Huang and Lingrui Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32703},
  eprint = {2609.32703},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32703},
}
RIS
TY  - UNPB
TI  - Non-analyticity of hairs of exponential maps
AU  - Weiwei Cui
AU  - Jiaxing Huang
AU  - Lingrui Wang
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32703
UR  - https://arxiv.org/abs/2609.32703
AB  - 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^∞. In this paper we show that hairs are not analytic except for trivial ones. This solves a long-standing open question.
ER  -