• Corpus ID: 204838261

# On the dimension spectra of infinite iterated function systems

@article{Das2019OnTD,
title={On the dimension spectra of infinite iterated function systems},
author={Tushar Das and David Simmons},
journal={arXiv: Dynamical Systems},
year={2019}
}
• Published 22 October 2019
• Mathematics
• arXiv: Dynamical Systems
The dimension spectrum of an iterated function system (IFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. We construct a compact perfect subset of the nonnegative reals that cannot be realized as the dimension spectrum of a conformal IFS. We also provide an example of a similarity IFS whose dimension spectrum has zero Hausdorff dimension; in particular, such a dimension spectrum is not uniformly perfect. This resolves two questions posed by Chousionis, Leykekhman…
1 Citations
Dimension spectrum of infinite self-affine iterated function systems
• N. Jurga
• Mathematics
Selecta Mathematica
• 2021
Given an infinite iterated function system (IFS) $${\mathcal {F}}$$ F , we define its dimension spectrum $$D({\mathcal {F}})$$ D ( F ) to be the set of real numbers which can be realised as the

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