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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.20632 |
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| _version_ | 1866914213393334272 |
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| author | Miao, Junjie Wang, Tianrui |
| author_facet | Miao, Junjie Wang, Tianrui |
| contents | Non-autonomous iterated function systems are a generalization of iterated function systems. If the contractions in the system are conformal mappings, it is called a non-autonomous conformal iterated function system, and its attractor is called a non-autonomous conformal set. In this paper, we study intermediate dimension spectra of non-autonomous conformal sets which provide a unifying framework for Hausdorff and box-counting dimensions. First, we obtain the intermediate dimension spectra formula of non-autonomous conformal sets by using upper and lower topological pressures. As a consequence, we obtain simplified forms of their Hausdorff, packing and box dimensions. Finally, we explore the Hausdorff dimensions of the non-autonomous infinite conformal iterated function systems which consists of countably many conformal mappings at each level, and we provide the Hausdorff dimension formula under certain conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20632 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimensions and dimension spectra of Non-autonomous iterated function systems Miao, Junjie Wang, Tianrui Dynamical Systems Non-autonomous iterated function systems are a generalization of iterated function systems. If the contractions in the system are conformal mappings, it is called a non-autonomous conformal iterated function system, and its attractor is called a non-autonomous conformal set. In this paper, we study intermediate dimension spectra of non-autonomous conformal sets which provide a unifying framework for Hausdorff and box-counting dimensions. First, we obtain the intermediate dimension spectra formula of non-autonomous conformal sets by using upper and lower topological pressures. As a consequence, we obtain simplified forms of their Hausdorff, packing and box dimensions. Finally, we explore the Hausdorff dimensions of the non-autonomous infinite conformal iterated function systems which consists of countably many conformal mappings at each level, and we provide the Hausdorff dimension formula under certain conditions. |
| title | Dimensions and dimension spectra of Non-autonomous iterated function systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2508.20632 |