On the dimension of $αβ$-sets
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910667520344064 |
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| author | Hochman, Michael |
| author_facet | Hochman, Michael |
| contents | We show that the Feng-Xiong lower bound of $1/2$ for the box dimension of $αβ$-sets is tight. We also study how much of an $αβ$-orbit ``carries the dimension'': deleting an arbitararily small positive density set of times can cause the box dimension to drop to zero, but the Assouad dimension cannot drop below $1/4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the dimension of $αβ$-sets Hochman, Michael Dynamical Systems Metric Geometry 28A80, 37C45, 11J13, 11J83 We show that the Feng-Xiong lower bound of $1/2$ for the box dimension of $αβ$-sets is tight. We also study how much of an $αβ$-orbit ``carries the dimension'': deleting an arbitararily small positive density set of times can cause the box dimension to drop to zero, but the Assouad dimension cannot drop below $1/4$. |
| title | On the dimension of $αβ$-sets |
| topic | Dynamical Systems Metric Geometry 28A80, 37C45, 11J13, 11J83 |
| url | https://arxiv.org/abs/2410.19640 |