Irregular set and metric mean dimension with potential
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866929436439347200 |
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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 a continuous function. In this paper, we consider the multifractal irregular set
\begin{align*}
I_φ=\left\{x\in X:\lim\limits_{n\to\infty}\frac{1}{n}\sum_{i=0}^{n-1}φ(f^ix)\ \text{does not exist}\right\}
\end{align*} and show that this set is either empty or carries full Bowen upper and lower metric mean dimension with potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17079 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Irregular set and metric mean dimension with potential Zhang, Tianlong Chen, Ercai Zhou, Xiaoyao Dynamical Systems Let $(X,f)$ be a dynamical system with the specification property and $φ$ be a continuous function. In this paper, we consider the multifractal irregular set \begin{align*} I_φ=\left\{x\in X:\lim\limits_{n\to\infty}\frac{1}{n}\sum_{i=0}^{n-1}φ(f^ix)\ \text{does not exist}\right\} \end{align*} and show that this set is either empty or carries full Bowen upper and lower metric mean dimension with potential. |
| title | Irregular set and metric mean dimension with potential |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2407.17079 |