Spectral cocycle for substitution tilings
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914787403759616 |
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| author | Solomyak, Boris Treviño, Rodrigo |
| author_facet | Solomyak, Boris Treviño, Rodrigo |
| contents | The construction of spectral cocycle from the case of 1-dimensional substitution flows by Bufetov-Solomyak [arXiv:1802.04783] is extended to the setting of pseudo-self-similar tilings in ${\mathbb R}^d$, allowing expanding similarities with rotations. The pointwise upper Lyapunov exponent of this cocycle is used to bound the local dimension of spectral measures of deformed tilings. The deformations are considered, following Treviño [arXiv:2006.16980], in the simpler, non-random setting. We review some of the results on quantitative weak mixing from [arXiv:2006.16980] in this special case and illustrate them on concrete examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_00749 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Spectral cocycle for substitution tilings Solomyak, Boris Treviño, Rodrigo Dynamical Systems 37B52, 37A30, 52C23 The construction of spectral cocycle from the case of 1-dimensional substitution flows by Bufetov-Solomyak [arXiv:1802.04783] is extended to the setting of pseudo-self-similar tilings in ${\mathbb R}^d$, allowing expanding similarities with rotations. The pointwise upper Lyapunov exponent of this cocycle is used to bound the local dimension of spectral measures of deformed tilings. The deformations are considered, following Treviño [arXiv:2006.16980], in the simpler, non-random setting. We review some of the results on quantitative weak mixing from [arXiv:2006.16980] in this special case and illustrate them on concrete examples. |
| title | Spectral cocycle for substitution tilings |
| topic | Dynamical Systems 37B52, 37A30, 52C23 |
| url | https://arxiv.org/abs/2201.00749 |