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 Julia sets of uniformly quasiregular mappings are uniformly perfect


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It is well-known that the Julia set Jf of a rational map is uniformly perfect; that is, every ring domain which separates Jf has bounded modulus, with the bound depending only on f. In this article we prove that an analogous result is true in higher dimensions; namely, that the Julia set Jf of a uniformly quasiregular mapping f in R^n is uniformly perfect. In particular, this implies that the Julia set of a uniformly quasiregular mapping has positive Hausdorff dimension.



Author: Alastair Fletcher; Daniel A. Nicks

Source: https://archive.org/







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