Multifractal analysis for the pointwise Assouad dimension of self-similar measures
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914634201563136 |
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| author | Anttila, Roope Suomala, Ville |
| author_facet | Anttila, Roope Suomala, Ville |
| contents | We quantify the pointwise doubling properties of self-similar measures using the notion of pointwise Assouad dimension. We show that all self-similar measures satisfying the open set condition are pointwise doubling in a set of full Hausdorff dimension, despite the fact that they can in general be non-doubling in a set of full Hausdorff measure. More generally, we carry out multifractal analysis by determining the Hausdorff dimension of the level sets of the pointwise Assouad dimension. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_03953 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multifractal analysis for the pointwise Assouad dimension of self-similar measures Anttila, Roope Suomala, Ville Dynamical Systems Classical Analysis and ODEs 28A80 (Primary), 37C45 (Secondary) We quantify the pointwise doubling properties of self-similar measures using the notion of pointwise Assouad dimension. We show that all self-similar measures satisfying the open set condition are pointwise doubling in a set of full Hausdorff dimension, despite the fact that they can in general be non-doubling in a set of full Hausdorff measure. More generally, we carry out multifractal analysis by determining the Hausdorff dimension of the level sets of the pointwise Assouad dimension. |
| title | Multifractal analysis for the pointwise Assouad dimension of self-similar measures |
| topic | Dynamical Systems Classical Analysis and ODEs 28A80 (Primary), 37C45 (Secondary) |
| url | https://arxiv.org/abs/2401.03953 |