Abstract
In this paper, we will consider subfractals, defined as a subset of the attractor of hyperbolic iterated function systems, which satisfy the open set condition. The subfractals will consist of points associated with infinite strings from a sofic subshift on the symbolic space. We find that the zeros of the lower and upper topological pressure functions are lower and upper bounds, respectively, for the Hausdorff, packing, lower and upper box dimensions of the subfractal.
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Acknowledgements
The author thanks her advisor, Doğan Çömez for his guidance and many helpful conversations during the construction of this paper. She is grateful to Michael P. Cohen for his edits and especially useful comments and to Mrinal Kanti Roychowdhury and Azer Akhmedov for their comments on an earlier preprint. She also thanks the reviewers for their thoughtful comments and suggestions.
Funding Funding was provided by Office of Experimental Program to Stimulate Competitive Research (1355466).
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Communicated by A. Constantin.
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Sattler, E. Fractal dimensions of subfractals induced by sofic subshifts. Monatsh Math 183, 539–557 (2017). https://doi.org/10.1007/s00605-017-1044-z
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DOI: https://doi.org/10.1007/s00605-017-1044-z