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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.13228 |
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| _version_ | 1866909448354660352 |
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| author | Marshall-Maldonado, Juan |
| author_facet | Marshall-Maldonado, Juan |
| contents | We study the regularity of spectral measures of dynamical systems arising from a translation action on tilings of substitutive nature. The results are inspired in the work of Bufetov and Solomyak, where they established a log-Hölder modulus of continuity of one-dimensional self-similar tiling systems. We generalize this result to higher dimensions in the more general setting of self-affine tilings systems. Further analysis leads to uniform estimates in the whole space of spectral parameters, allowing to deduce logarithmic rates of weak mixing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13228 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative weak mixing of self-affine tilings Marshall-Maldonado, Juan Dynamical Systems We study the regularity of spectral measures of dynamical systems arising from a translation action on tilings of substitutive nature. The results are inspired in the work of Bufetov and Solomyak, where they established a log-Hölder modulus of continuity of one-dimensional self-similar tiling systems. We generalize this result to higher dimensions in the more general setting of self-affine tilings systems. Further analysis leads to uniform estimates in the whole space of spectral parameters, allowing to deduce logarithmic rates of weak mixing. |
| title | Quantitative weak mixing of self-affine tilings |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2408.13228 |