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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
3 articles.
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1. Julia sets of Zorich maps;Ergodic Theory and Dynamical Systems;2021-11-15
2. Non-escaping points of Zorich maps;Israel Journal of Mathematics;2021-05-07
3. Nowhere differentiable hairs for entire maps;Mathematische Zeitschrift;2018-12-17