On the dimension spectra of infinite iterated function systems
Dynamical Systems
2023-02-24 v3
Abstract
The dimension spectrum of a conformal iterated function system (CIFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. This brief note provides two constructions -- (i) a compact perfect set that cannot be realized as the dimension spectrum of a CIFS; and (ii) a similarity IFS whose dimension spectrum has zero Hausdorff dimension, and thus is not uniformly perfect -- which resolve questions posed by Chousionis, Leykekhman, and Urba\'nski, and go on provoke fresh conjectures and questions regarding the topological and metric properties of IFS dimension spectra.
Cite
@article{arxiv.1910.10259,
title = {On the dimension spectra of infinite iterated function systems},
author = {Tushar Das and David Simmons},
journal= {arXiv preprint arXiv:1910.10259},
year = {2023}
}