Iterated function system quasiarcs

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 and 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:

02 Aug 2017 15:47

Publisher DOI:

10.1090/ecgd/305

BORIS DOI:

10.7892/boris.97575

URI:

https://boris.unibe.ch/id/eprint/97575

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