Dimensions and dimension spectra of Non-autonomous iterated function systems
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914213393334272 |
|---|---|
| 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 |