Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.13075 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914201733169152 |
|---|---|
| author | Ding, Zhumin Yang, Rui Zhou, Xiaoyao |
| author_facet | Ding, Zhumin Yang, Rui Zhou, Xiaoyao |
| contents | We aim to investigate the dimension theory of $α$-pressure-like quantities. By means of the Carath$\acute{\rm e}$odory-Pesin structure, we define $α$-BS dimension and $α$-Pesin topological pressure on subsets using $α$-Bowen metric $$d_{n}^α(x,y)=\max_{0\leq i\leq n-1}e^{αi}d(f^{i}x,f^{i}y),$$ where $α\geq 0$. Specifically, we show that $α$-BS dimension and $α$-Pesin topological pressure are related by a Bowen's equation. Inspired by the classical Brin-Katok entropy, we introduce the notion of $α$-local Brin-Katok entropy, and establish a variational principle for $α$-BS dimension on compact subsets in terms of $α$-local Brin-Katok entropy. Besides, for subshifts of finite type, we prove that $α$-Bowen topological entropy is closely related to spectral radius and Hausdorff dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13075 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $α$-BS dimension on subsets Ding, Zhumin Yang, Rui Zhou, Xiaoyao Dynamical Systems We aim to investigate the dimension theory of $α$-pressure-like quantities. By means of the Carath$\acute{\rm e}$odory-Pesin structure, we define $α$-BS dimension and $α$-Pesin topological pressure on subsets using $α$-Bowen metric $$d_{n}^α(x,y)=\max_{0\leq i\leq n-1}e^{αi}d(f^{i}x,f^{i}y),$$ where $α\geq 0$. Specifically, we show that $α$-BS dimension and $α$-Pesin topological pressure are related by a Bowen's equation. Inspired by the classical Brin-Katok entropy, we introduce the notion of $α$-local Brin-Katok entropy, and establish a variational principle for $α$-BS dimension on compact subsets in terms of $α$-local Brin-Katok entropy. Besides, for subshifts of finite type, we prove that $α$-Bowen topological entropy is closely related to spectral radius and Hausdorff dimension. |
| title | $α$-BS dimension on subsets |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2512.13075 |