Dimension spectrum of infinite self-affine iterated function systems
Abstract
Given an infinite iterated function system (IFS) F, we define its dimension spectrum D(F) to be the set of real numbers which can be realised as the dimension of some subsystem of F. In the case where FF is a conformal IFS, the properties of the dimension spectrum have been studied by several authors. In this paper we investigate for the first time the properties of the dimension spectrum when F is a non-conformal IFS. In particular, unlike dimension spectra of conformal IFS which are always compact and perfect (by a result of Chousionis, Leykekhman and Urbański, Selecta 2019), we construct examples to show that D(F) need not be compact and may contain isolated points.
Citation
Jurga , N A 2021 , ' Dimension spectrum of infinite self-affine iterated function systems ' , Selecta Mathematica: New Series , vol. 27 , no. 3 , 49 . https://doi.org/10.1007/s00029-021-00674-x
Publication
Selecta Mathematica: New Series
Status
Peer reviewed
ISSN
1420-9020Type
Journal article
Rights
Copyright © The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Description
Funding: The author was financially supported by the Leverhulme Trust (Research Project Grant number RPG-2016-194) and by the EPSRC (Standard Grant EP/R015104/1).Collections
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