Mean Assouad dimension and spectrum, with applications to infinite dimensional fractals
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918268759965696 |
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| author | Huo, Qiang Śpiewak, Adam |
| author_facet | Huo, Qiang Śpiewak, Adam |
| contents | We introduce the mean Assouad dimension of a dynamical system, motivated by the Assouad dimension in fractal geometry. Using dimension interpolation, we further define the mean Assouad spectrum. This provides a new family of bi-Lipschitz invariants of dynamical systems. We study its basic properties and calculate it for several classes of dynamical systems. As an application, we determine explicit formulae for the mean Assouad dimension and spectrum of infinite-dimensional Bedford--McMullen carpet systems, contributing to the program of studying infinite dimensional fractals, initiated recently by Tsukamoto. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00233 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mean Assouad dimension and spectrum, with applications to infinite dimensional fractals Huo, Qiang Śpiewak, Adam Dynamical Systems Classical Analysis and ODEs 28A80, 37B40, 37C45, 37B10 We introduce the mean Assouad dimension of a dynamical system, motivated by the Assouad dimension in fractal geometry. Using dimension interpolation, we further define the mean Assouad spectrum. This provides a new family of bi-Lipschitz invariants of dynamical systems. We study its basic properties and calculate it for several classes of dynamical systems. As an application, we determine explicit formulae for the mean Assouad dimension and spectrum of infinite-dimensional Bedford--McMullen carpet systems, contributing to the program of studying infinite dimensional fractals, initiated recently by Tsukamoto. |
| title | Mean Assouad dimension and spectrum, with applications to infinite dimensional fractals |
| topic | Dynamical Systems Classical Analysis and ODEs 28A80, 37B40, 37C45, 37B10 |
| url | https://arxiv.org/abs/2601.00233 |