Dimension of contracting on average self-similar measures
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912209475469312 |
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| author | Kittle, Samuel Kogler, Constantin |
| author_facet | Kittle, Samuel Kogler, Constantin |
| contents | We generalise Hochman's theorem on the dimension of self-similar measures to contracting on average measures and show that a weaker condition than exponential separation on all scales is sufficient. Our proof uses a technique we call the variance summation method, avoiding the use of inverse theorems for entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension of contracting on average self-similar measures Kittle, Samuel Kogler, Constantin Dynamical Systems Classical Analysis and ODEs Probability We generalise Hochman's theorem on the dimension of self-similar measures to contracting on average measures and show that a weaker condition than exponential separation on all scales is sufficient. Our proof uses a technique we call the variance summation method, avoiding the use of inverse theorems for entropy. |
| title | Dimension of contracting on average self-similar measures |
| topic | Dynamical Systems Classical Analysis and ODEs Probability |
| url | https://arxiv.org/abs/2501.17795 |