Non-analyticity of hairs of exponential maps

Abstract

Let $f_{\lambda }(z)=\lambda e^z$, where $0<\lambda <1/e$. 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.

arXiv comment7 pages; comments welcome