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Julia sets of uniformly quasiregular mappings are uniformly perfect
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Fletcher, Alastair N. and Nicks, Daniel A. (2011) Julia sets of uniformly quasiregular mappings are uniformly perfect. Mathematical Proceedings of the Cambridge Philosophical Society, Vol.151 (No.3). pp. 541-550. doi:10.1017/S0305004111000478 ISSN 0305-0041.
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Official URL: http://dx.doi.org/10.1017/S0305004111000478
Abstract
It is well known that the Julia set J(f) of a rational map f: ℂ → ℂ is uniformly perfect; that is, every ring domain which separates J(f) has bounded modulus, with the bound depending only on f. In this paper we prove that an analogous result is true in higher dimensions; namely, that the Julia set J(f) of a uniformly quasiregular mapping f: ℝn → ℝn is uniformly perfect. In particular, this implies that the Julia set of a uniformly quasiregular mapping has positive Hausdorff dimension.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Mathematical Proceedings of the Cambridge Philosophical Society | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0305-0041 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.151 | ||||
Number: | No.3 | ||||
Number of Pages: | 10 | ||||
Page Range: | pp. 541-550 | ||||
DOI: | 10.1017/S0305004111000478 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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