# On the differentiability of hairs for Zorich maps

## TL;DR

This paper extends the smoothness results of Julia set curves from exponential maps to Zorich maps, a quasiregular analogue, demonstrating their differentiability.

## Contribution

It generalizes Viana's smoothness result from exponential maps to Zorich maps, a quasiregular class, establishing differentiability of Julia set curves.

## Key findings

- Julia set curves are smooth for Zorich maps
- Generalization of exponential map results to quasiregular maps
- Differentiability of hairs in Zorich maps

## Abstract

Devaney and Krych showed that for the exponential family $\lambda e^z$, where $0<\lambda <1/e$, the Julia set consists of uncountably many pairwise disjoint simple curves tending to $\infty$. Viana proved that these curves are smooth. In this article we consider a quasiregular counterpart of the exponential map, the so-called Zorich maps, and generalize Viana's result to these maps.