## Iterated function system quasiarcs

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- by Annina Iseli and Kevin Wildrick
- Conform. Geom. Dyn.
**21**(2017), 78-100 - DOI: https://doi.org/10.1090/ecgd/305
- Published electronically: February 3, 2017
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## Abstract:

We consider a class of iterated function systems (IFSs) of contracting similarities of $\mathbb {R}^n$, introduced by Hutchinson, for which the invariant set possesses a natural Hölder continuous parameterization by the unit interval. When such an invariant set is homeomorphic to an interval, we give necessary conditions in terms of the similarities alone for it to possess a quasisymmetric (and as a corollary, bi-Hölder) parameterization. We also give a related necessary condition for the invariant set of such an IFS to be homeomorphic to an interval.## References

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## Bibliographic Information

**Annina Iseli**- Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
- Email: annina.iseli@math.unibe.ch
**Kevin Wildrick**- Affiliation: Department of Mathematical Sciences, Montana State University, P.O. Box 172400 Bozeman, Montana 59717
- MR Author ID: 843465
- Email: kevin.wildrick@montana.edu
- Received by editor(s): November 20, 2015
- Received by editor(s) in revised form: November 25, 2016
- Published electronically: February 3, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**21**(2017), 78-100 - MSC (2010): Primary 28A80, 30C65
- DOI: https://doi.org/10.1090/ecgd/305
- MathSciNet review: 3604862