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15 September 2010 Karpińska's paradox in dimension 3
Walter Bergweiler
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Duke Math. J. 154(3): 599-630 (15 September 2010). DOI: 10.1215/00127094-2010-047

Abstract

It was proved by Devaney and Krych, by McMullen, and by Karpińska that, for 0<λ<1/e, the Julia set of λez is an uncountable union of pairwise disjoint simple curves tending to infinity, and the Hausdorff dimension of this set is 2, but the set of curves without endpoints has Hausdorff dimension 1. We show that these results have 3-dimensional analogues when the exponential function is replaced by a quasi-regular self-map of R3 introduced by Zorich.

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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

Information

Published: 15 September 2010
First available in Project Euclid: 7 September 2010

zbMATH: 1218.37057
MathSciNet: MR2730579
Digital Object Identifier: 10.1215/00127094-2010-047

Subjects:
Primary: 37F35
Secondary: 30C65, 30D05, 37F10

Rights: Copyright © 2010 Duke University Press

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Vol.154 • No. 3 • 15 September 2010
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