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Conformal Geometry and Dynamics

ISSN 1088-4173

 

 

Iterated function system quasiarcs


Authors: Annina Iseli and Kevin Wildrick
Journal: Conform. Geom. Dyn. 21 (2017), 78-100
MSC (2010): Primary 28A80, 30C65
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.


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Additional 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
Email: kevin.wildrick@montana.edu

DOI: https://doi.org/10.1090/ecgd/305
Received by editor(s): November 20, 2015
Received by editor(s) in revised form: November 25, 2016
Published electronically: February 3, 2017
Article copyright: © Copyright 2017 American Mathematical Society