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On the differentiability of hairs for Zorich maps

Published online by Cambridge University Press:  07 November 2017

PATRICK COMDÜHR
PATRICK COMDÜHR*
Affiliation:
Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany email comduehr@math.uni-kiel.de
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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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 7 , July 2019 , pp. 1824 - 1842
Copyright
© Cambridge University Press, 2017 

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