Genus 2 Cantor sets
| Autor: | Fletcher, Alastair N., Stoertz, Daniel |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Pacific J. Math. 321 (2022) 283-307 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/pjm.2022.321.283 |
| Popis: | We construct a geometrically self-similar Cantor set $X$ of genus $2$ in $\mathbb{R}^3$. This construction is the first for which the local genus is shown to be $2$ at every point of $X$. As an application, we construct, also for the first time, a uniformly quasiregular mapping $f:\mathbb{R}^3 \to \mathbb{R}^3$ for which the Julia set $J(f)$ is a genus $2$ Cantor set. Comment: 20 pages, 6 figures |
| Databáze: | arXiv |
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