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<p>In this paper, we explore expansive measures and expansiveness within the context of nonautonomous iterated function systems. Specifically, we demonstrate that the set of expansive measures for any nonautonomous iterated function system forms a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2024_1216_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_{\delta \sigma }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mrow> <mi>δ</mi> <mi>σ</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> subset of the set of all Borel measures.</p>

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Expansive Measures of Nonautonomous Iterated Function Systems

  • 期刊论文

  • 发表日期：

    2025年1月27日

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  • Mengxin Cui,
  • Bilel Selmi,
  • Zhiming Li

摘要

In this paper, we explore expansive measures and expansiveness within the context of nonautonomous iterated function systems. Specifically, we demonstrate that the set of expansive measures for any nonautonomous iterated function system forms a \(G_{\delta \sigma }\) G δ σ subset of the set of all Borel measures.