Local dimension spectrum for dominated planar self-affine sets
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908773573984256 |
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| author | Batsis, Alex Käenmäki, Antti Kempton, Tom |
| author_facet | Batsis, Alex Käenmäki, Antti Kempton, Tom |
| contents | The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated self-affine measures. By analyzing exact dimensionality, we obtain deterministic results that extend the scope of the local dimension spectrum beyond the almost-sure setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13626 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local dimension spectrum for dominated planar self-affine sets Batsis, Alex Käenmäki, Antti Kempton, Tom Dynamical Systems Classical Analysis and ODEs The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated self-affine measures. By analyzing exact dimensionality, we obtain deterministic results that extend the scope of the local dimension spectrum beyond the almost-sure setting. |
| title | Local dimension spectrum for dominated planar self-affine sets |
| topic | Dynamical Systems Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2401.13626 |