# 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…

## One Citation

Dimension spectrum of infinite self-affine iterated function systems

- MathematicsSelecta 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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