Uniformly quasiregular maps of $\mathbb{R}^n$ with Cantor Julia sets

Daniel A. Nicks

Uniformly quasiregular maps of $\mathbb{R}^n$ with Cantor Julia sets

Dynamical Systems 2026-07-24 v1

Authors: Daniel A. Nicks

Abstract

For any $n\ge 3$ , we construct uniformly quasiregular self-maps of $\mathbb{R}^n$ of polynomial type for which the Julia set is a Cantor set.

Keywords

uniformly quasiregular maps cantor julia sets polynomial type iteration theory higher dimensions

Cite

@article{arxiv.2607.22223,
  title  = {Uniformly quasiregular maps of $\mathbb{R}^n$ with Cantor Julia sets},
  author = {Daniel A. Nicks},
  journal= {arXiv preprint arXiv:2607.22223},
  year   = {2026}
}

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7 pages