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arXiv · 2403.15608

Hausdorff and box dimension bounds for subfractals induced by $S$-gap shifts

Elizabeth Sattler
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Abstract

In this paper, we consider subsets of an attractor of an iterated function system in which each point is associated with an allowable word from an $S$-gap shift. The main result shows that bounds for the box dimension and Hausdorff dimension of a subfractal induced by an $S$-gap shift are given by the zeros of the upper and lower topological pressure functions.

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Elizabeth Sattler. 2024-03-22. Hausdorff and box dimension bounds for subfractals induced by $S$-gap shifts. https://arxiv.org/abs/2403.15608

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