JournalsjfgVol. 9, No. 1/2pp. 73–87

On the dimension spectra of infinite conformal iterated function systems

  • Tushar Das

    University of Wisconsin – La Crosse, USA

  • David Simmons

    University of York, UK
On the dimension spectra of infinite conformal iterated function systems cover
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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 Urbański, and goes on to provoke fresh conjectures and questions regarding the topological and metric properties of IFS dimension spectra.

Cite this article

Tushar Das, David Simmons, On the dimension spectra of infinite conformal iterated function systems. J. Fractal Geom. 9 (2022), no. 1/2, pp. 73–87

DOI 10.4171/JFG/112