Julia sets of uniformly quasiregular mappings are uniformly perfect
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. ISSN 0305-0041Full text not available from this repository.
Official URL: http://dx.doi.org/10.1017/S0305004111000478
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|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publisher:||Cambridge University Press|
|Number of Pages:||10|
|Page Range:||pp. 541-550|
|Access rights to Published version:||Restricted or Subscription Access|
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