On the dimension of orthogonal projections of self-similar measures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911964890923008 |
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| author | Algom, Amir Shmerkin, Pablo |
| author_facet | Algom, Amir Shmerkin, Pablo |
| contents | Let $ν$ be a self similar measure on $\mathbb{R}^d$, $d\geq 2$, and let $π$ be an orthogonal projection onto a $k$-dimensional subspace. We formulate a criterion on the action of the group generated by the orthogonal parts of the IFS on $π$, and show that it ensures the dimension of $πν$ is preserved; this significantly refines previous results by Hochman-Shmerkin (2012) and Falconer-Jin (2014), and is sharp for projections to lines and hyperplanes. A key ingredient in the proof is an application of a restricted projection theorem of Gan-Guo-Wang (2024). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16262 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the dimension of orthogonal projections of self-similar measures Algom, Amir Shmerkin, Pablo Dynamical Systems Classical Analysis and ODEs Let $ν$ be a self similar measure on $\mathbb{R}^d$, $d\geq 2$, and let $π$ be an orthogonal projection onto a $k$-dimensional subspace. We formulate a criterion on the action of the group generated by the orthogonal parts of the IFS on $π$, and show that it ensures the dimension of $πν$ is preserved; this significantly refines previous results by Hochman-Shmerkin (2012) and Falconer-Jin (2014), and is sharp for projections to lines and hyperplanes. A key ingredient in the proof is an application of a restricted projection theorem of Gan-Guo-Wang (2024). |
| title | On the dimension of orthogonal projections of self-similar measures |
| topic | Dynamical Systems Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2407.16262 |