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On the differentiability of hairs for Zorich maps
Published online by Cambridge University Press: 07 November 2017
Abstract
Devaney and Krych showed that, for the exponential family $\unicode[STIX]{x1D706}e^{z}$, where
$0\,<\,\unicode[STIX]{x1D706}\,<\,1/e$, 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 quasiregular counterparts of the exponential map, the so-called Zorich maps, and generalize Viana’s result to these maps.
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