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- W3014242207 abstract "It is well-known that the Julia set of a hyperbolic rational map is quasisymmetrically equivalent to the standard Cantor set. Using the uniformization theorem of David and Semmes, this result comes down to the fact that such a Julia set is both uniformly perfect and uniformly disconnected. We study the analogous question for Julia sets of UQR maps in $mathbb{S}^n$, for $ngeq 2$. Introducing hyperbolic UQR maps, we show that the Julia set of such a map is uniformly disconnected if it is totally disconnected. Moreover, we show that if $E$ is a compact, uniformly perfect and uniformly disconnected set in $mathbb{S}^n$, then it is the Julia set of a hyperbolic UQR map $f:mathbb{S}^N to mathbb{S}^N$ where $N=n$ if $n=2$ and $N=n+1$ otherwise." @default.
- W3014242207 created "2020-04-10" @default.
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- W3014242207 date "2020-04-03" @default.
- W3014242207 modified "2023-09-28" @default.
- W3014242207 title "On uniformly disconnected Julia sets" @default.
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