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<p>Lindenstrauss and Tsukamoto in 2019 established double variational principle for mean dimension. In this paper, we focus on developing the mean dimension theory for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2025_452_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {Z}}^k\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mi>k</mi> </msup> </math></EquationSource> </InlineEquation>-actions. Specifically, we establish a double variational principle for mean dimension of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2025_452_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {Z}}^k\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mi>k</mi> </msup> </math></EquationSource> </InlineEquation>-actions for dynamical systems with the marker property.</p>

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Double Variational Principle of Mean Dimension for \({\mathbb {Z}}^{k}\)-Actions

  • 期刊论文

  • 发表日期：

    2025年8月9日

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  • Yunping Wang,
  • Ercai Chen

摘要

Lindenstrauss and Tsukamoto in 2019 established double variational principle for mean dimension. In this paper, we focus on developing the mean dimension theory for \({\mathbb {Z}}^k\) Z k -actions. Specifically, we establish a double variational principle for mean dimension of \({\mathbb {Z}}^k\) Z k -actions for dynamical systems with the marker property.