References & Citations
Mathematics > Dynamical Systems
Title: Double variational principle for mean dimension of $\mathbb{Z}^{K}$-actions
(Submitted on 4 Oct 2023 (v1), last revised 18 Jan 2024 (this version, v2))
Abstract: In this paper, we introduce mean dimension and rate distortion dimension for $\mathbb{Z}^{k}$-actions dynamical system $(\mathcal{X},\mathbb{Z}^k,T)$. Suppose $(\mathcal{X},\mathbb{Z}^k,T)$ has the marker property. Taking these two variables, the metric $d$ on $\mathcal{X}$ and $\mathbb{Z}^{k}$-invariant measure $\mu$, into consideration, a minimax-type variational principle for mean dimension of $\mathbb{Z}^{k}$-actions is established. This result extends the double variational principle obtained recently by Lindenstrauss and Tsukamoto \cite{LT19} from $\mathbb{Z}$-actions dynamical systems to $\mathbb{Z}^{k}$-actions dynamical systems.
Submission history
From: Qiang Huo [view email][v1] Wed, 4 Oct 2023 22:35:48 GMT (34kb)
[v2] Thu, 18 Jan 2024 14:18:15 GMT (0kb,I)
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