Attractor sets and Julia sets in low dimensions

Fletcher, A.

doi:10.1090/ecgd/334

Attractor sets and Julia sets in low dimensions
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by A. Fletcher

Conform. Geom. Dyn. 23 (2019), 117-129

DOI: https://doi.org/10.1090/ecgd/334

Published electronically: June 25, 2019

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Abstract:

If $X$ is the attractor set of a conformal IFS (iterated function system) in dimension two or three, we prove that there exists a quasiregular semigroup $G$ with a Julia set equal to $X$. We also show that in dimension two, with a further assumption similar to the open set condition, the same result can be achieved with a semigroup generated by one element. Consequently, in this case the attractor set is quasiconformally equivalent to the Julia set of a rational map.

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