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Abstract <p> In this paper, we introduce and study concepts of mean equicontinuity and mean sensitivity via Furstenberg family with respect to a countable left amenable semigroup <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(S\)</EquationSource> </InlineEquation>, We also present an analogue of the Auslander–Yorke dichotomy, demonstrating that a transitive system either has <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathscr{F}\)</EquationSource> </InlineEquation>-mean sensitive pair almost everywhere or is almost <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\kappa\mathscr{F}\)</EquationSource> </InlineEquation>-mean equicontinuous. Also, we prove that the definition of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathscr{F}\)</EquationSource> </InlineEquation>-mean equicontinuity is preserved by an open factor map. </p>

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\(\mathscr{F}\)-Mean Equicontinuity on Amenable Semigroups

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • J. Jafari,
  • M. A. Tootkaboni,
  • A. Sahleh

摘要

Abstract

In this paper, we introduce and study concepts of mean equicontinuity and mean sensitivity via Furstenberg family with respect to a countable left amenable semigroup \(S\) , We also present an analogue of the Auslander–Yorke dichotomy, demonstrating that a transitive system either has \(\mathscr{F}\) -mean sensitive pair almost everywhere or is almost \(\kappa\mathscr{F}\) -mean equicontinuous. Also, we prove that the definition of \(\mathscr{F}\) -mean equicontinuity is preserved by an open factor map.