Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Cui, Weiwei, Huang, Jiaxing, Wang, Lingrui
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1307562068, G2922846622, G5268949154
OpenAlex ID: W7214709613