Iseli, Annina; Wildrick, Kevin Michael (2017). Iterated function system quasiarcs. Conformal geometry and dynamics, 21(3), pp. 78-100. American Mathematical Society 10.1090/ecgd/305
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We consider a class of iterated function systems (IFSs) of contracting similarities of Rn, 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.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Iseli, Annina, Wildrick, Kevin Michael |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1088-4173 |
Publisher: |
American Mathematical Society |
Language: |
English |
Submitter: |
Olivier Bernard Mila |
Date Deposited: |
02 Aug 2017 15:47 |
Last Modified: |
05 Dec 2022 15:04 |
Publisher DOI: |
10.1090/ecgd/305 |
BORIS DOI: |
10.7892/boris.97575 |
URI: |
https://boris.unibe.ch/id/eprint/97575 |
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