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arXiv · 1910.10259

On the dimension spectra of infinite iterated function systems

Tushar Das·David Simmons
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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 go on provoke fresh conjectures and questions regarding the topological and metric properties of IFS dimension spectra.

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Tushar Das, David Simmons. 2020-09-20. On the dimension spectra of infinite iterated function systems. https://doi.org/10.4171/jfg%2F112

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