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arXiv · 1701.06873

On the differentiability of hairs for Zorich maps

Patrick Comdühr
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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.

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Patrick Comdühr. 2017-01-24. On the differentiability of hairs for Zorich maps. https://doi.org/10.1017/etds.2017.104

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