Birkhoff spectrum for diagonally self-affine sets and digit frequencies for GLS systems with redundancy
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915056507158528 |
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| author | Imbierski, Jonny Kalle, Charlene Mohammadpour, Reza |
| author_facet | Imbierski, Jonny Kalle, Charlene Mohammadpour, Reza |
| contents | In this article, we calculate the Birkhoff spectrum in terms of the Hausdorff dimension of level sets for Birkhoff averages of continuous potentials for a certain family of diagonally affine IFS's. Also, we study Besicovitch-Eggleston sets for finite GLS number systems with redundancy. The redundancy refers to the fact that each number $x \in [0,1]$ has uncountably many expansions in the system. We determine the Hausdorff dimension of digit frequency sets for such expansions along fibres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15265 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Birkhoff spectrum for diagonally self-affine sets and digit frequencies for GLS systems with redundancy Imbierski, Jonny Kalle, Charlene Mohammadpour, Reza Dynamical Systems 11K55, 28A80, 37D35 In this article, we calculate the Birkhoff spectrum in terms of the Hausdorff dimension of level sets for Birkhoff averages of continuous potentials for a certain family of diagonally affine IFS's. Also, we study Besicovitch-Eggleston sets for finite GLS number systems with redundancy. The redundancy refers to the fact that each number $x \in [0,1]$ has uncountably many expansions in the system. We determine the Hausdorff dimension of digit frequency sets for such expansions along fibres. |
| title | Birkhoff spectrum for diagonally self-affine sets and digit frequencies for GLS systems with redundancy |
| topic | Dynamical Systems 11K55, 28A80, 37D35 |
| url | https://arxiv.org/abs/2310.15265 |