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arXiv · 2407.15027

Multifractal level sets and metric mean dimension with potential

Tianlong Zhang·Ercai Chen·Xiaoyao Zhou
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Abstract

Let $(X,f)$ be a dynamical system with the specification property and $\varphi$ 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 $K_\alpha:=\{x\in X:\lim\limits_{n\to\infty}\dfrac{1}{n}\sum\limits_{i=0}^{n-1}\varphi(f^ix)=\alpha\}.$

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Tianlong Zhang, Ercai Chen, Xiaoyao Zhou. 2024-07-21. Multifractal level sets and metric mean dimension with potential. https://arxiv.org/abs/2407.15027

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