## Attractor sets and Julia sets in low dimensions

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- by A. Fletcher PDF
- Conform. Geom. Dyn.
**23**(2019), 117-129 Request permission

## 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.## References

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## Additional Information

**A. Fletcher**- Affiliation: Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois 60115
- MR Author ID: 749646
- Email: fletcher@math.niu.edu
- Received by editor(s): October 23, 2018
- Received by editor(s) in revised form: March 6, 2019, and May 6, 2019
- Published electronically: June 25, 2019
- Additional Notes: This work was supported by a grant from the Simons Foundation (#352034, Alastair Fletcher).
- © Copyright 2019 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**23**(2019), 117-129 - MSC (2010): Primary 30D05; Secondary 30C62, 30C65
- DOI: https://doi.org/10.1090/ecgd/334
- MathSciNet review: 3973918