Graph Iterated Function Systems and Fractal Tops
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910315858362368 |
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| author | Lancaster-Cole, Grover Lyall, Georgiana Malcolm, Thomas Zhou, Qiyu |
| author_facet | Lancaster-Cole, Grover Lyall, Georgiana Malcolm, Thomas Zhou, Qiyu |
| contents | Following the work of Louisa and Michael Barnsley on results in tops of iterated function systems, we extend their work to graph-directed iterated function systems by investigating the relationship between top addresses and shift spaces. For the simplest overlapping interval IFS, we find a sufficient condition for the closure of its tops code space to be a shift space of finite type. Likewise, we find that shift invariance properties do not directly extend to the graph-directed setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graph Iterated Function Systems and Fractal Tops Lancaster-Cole, Grover Lyall, Georgiana Malcolm, Thomas Zhou, Qiyu Dynamical Systems 28A80 Following the work of Louisa and Michael Barnsley on results in tops of iterated function systems, we extend their work to graph-directed iterated function systems by investigating the relationship between top addresses and shift spaces. For the simplest overlapping interval IFS, we find a sufficient condition for the closure of its tops code space to be a shift space of finite type. Likewise, we find that shift invariance properties do not directly extend to the graph-directed setting. |
| title | Graph Iterated Function Systems and Fractal Tops |
| topic | Dynamical Systems 28A80 |
| url | https://arxiv.org/abs/2402.00237 |