• 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}
}
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
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