Hausdorff and box dimension bounds for subfractals induced by $S$-gap shifts
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914726020120576 |
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| author | Sattler, Elizabeth |
| author_facet | Sattler, Elizabeth |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15608 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hausdorff and box dimension bounds for subfractals induced by $S$-gap shifts Sattler, Elizabeth Dynamical Systems 28A80 (Primary), 37B10 (Secondary) 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. |
| title | Hausdorff and box dimension bounds for subfractals induced by $S$-gap shifts |
| topic | Dynamical Systems 28A80 (Primary), 37B10 (Secondary) |
| url | https://arxiv.org/abs/2403.15608 |