Multifractal level sets and metric mean dimension with potential
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914880256212992 |
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| author | Zhang, Tianlong Chen, Ercai Zhou, Xiaoyao |
| author_facet | Zhang, Tianlong Chen, Ercai Zhou, Xiaoyao |
| contents | Let $(X,f)$ be a dynamical system with the specification property and $φ$ be continuous functions. In this paper, we establish some conditional variational principles for the upper and lower Bowen/packing metric mean dimension with potential of multifractal level set $K_α:=\{x\in X:\lim\limits_{n\to\infty}\dfrac{1}{n}\sum\limits_{i=0}^{n-1}φ(f^ix)=α\}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15027 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multifractal level sets and metric mean dimension with potential Zhang, Tianlong Chen, Ercai Zhou, Xiaoyao Dynamical Systems 37A15, 37C45 Let $(X,f)$ be a dynamical system with the specification property and $φ$ be continuous functions. In this paper, we establish some conditional variational principles for the upper and lower Bowen/packing metric mean dimension with potential of multifractal level set $K_α:=\{x\in X:\lim\limits_{n\to\infty}\dfrac{1}{n}\sum\limits_{i=0}^{n-1}φ(f^ix)=α\}.$ |
| title | Multifractal level sets and metric mean dimension with potential |
| topic | Dynamical Systems 37A15, 37C45 |
| url | https://arxiv.org/abs/2407.15027 |