A multifractal analysis for uniform level sets with constraints on word appearance
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911045948276736 |
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| author | Liu, Ziyu |
| author_facet | Liu, Ziyu |
| contents | Given a topologically transitive subshift of finite type, the $u$-dimension of the $α$-level set of the quotient of Birkhoff sums is a well-studied topic. In this paper, we consider the uniform $α$-level set, which is a subset of the $α$-level set. We shall show that the $α$-level set and the uniform $α$-level set have the same $u$-dimension. Moreover, we also consider two types of subsets of the $α$-level set, whose elements are sequences satisfying some constraints on their subwords. We shall show that for $α$ not on the boundary of the dimension spectrum, these subsets also have the same $u$-dimension as the $α$-level set. As an application, we shall perform a multifractal analysis of the Hoelder regularity of a Gibbs measure on a one-dimensional manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17335 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A multifractal analysis for uniform level sets with constraints on word appearance Liu, Ziyu Dynamical Systems 37D35, 28A80 Given a topologically transitive subshift of finite type, the $u$-dimension of the $α$-level set of the quotient of Birkhoff sums is a well-studied topic. In this paper, we consider the uniform $α$-level set, which is a subset of the $α$-level set. We shall show that the $α$-level set and the uniform $α$-level set have the same $u$-dimension. Moreover, we also consider two types of subsets of the $α$-level set, whose elements are sequences satisfying some constraints on their subwords. We shall show that for $α$ not on the boundary of the dimension spectrum, these subsets also have the same $u$-dimension as the $α$-level set. As an application, we shall perform a multifractal analysis of the Hoelder regularity of a Gibbs measure on a one-dimensional manifold. |
| title | A multifractal analysis for uniform level sets with constraints on word appearance |
| topic | Dynamical Systems 37D35, 28A80 |
| url | https://arxiv.org/abs/2303.17335 |