Abstract
It was proved by Devaney and Krych, by McMullen, and by Karpińska that, for , the Julia set of is an uncountable union of pairwise disjoint simple curves tending to infinity, and the Hausdorff dimension of this set is , but the set of curves without endpoints has Hausdorff dimension . We show that these results have -dimensional analogues when the exponential function is replaced by a quasi-regular self-map of introduced by Zorich.
Citation
Walter Bergweiler. "Karpińska's paradox in dimension 3." Duke Math. J. 154 (3) 599 - 630, 15 September 2010. https://doi.org/10.1215/00127094-2010-047
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