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<p>The existence of non uniquely ergodic minimal interval exchange transformations with flips was proved in [<CitationRef CitationID="CR16">16</CitationRef>] by constructing (10,&#xa0;<i>k</i>)-IETs, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1347_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="81" /> </InlineMediaObject> <EquationSource Format="TEX">\(1\le k\le 10\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>k</mi> <mo>≤</mo> <mn>10</mn> </mrow> </math></EquationSource> </InlineEquation>. In this paper, we improve the technique of the construction, by the use of the so-called projetive pseudo-metric, and we get non uniquely ergodic minimal (6,&#xa0;<i>k</i>)-IETs, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1347_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="73" /> </InlineMediaObject> <EquationSource Format="TEX">\(1\le k\le 6\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>k</mi> <mo>≤</mo> <mn>6</mn> </mrow> </math></EquationSource> </InlineEquation>. Moreover, we introduce some general technical lemmas that will be useful to build new examples.</p>

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On Non Uniquely Ergodic Minimal IETs With Flips

  • 期刊论文

  • 发表日期：

    2025年7月25日

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  • Antonio Linero Bas,
  • Gabriel Soler López

摘要

The existence of non uniquely ergodic minimal interval exchange transformations with flips was proved in [16] by constructing (10, k)-IETs, \(1\le k\le 10\) 1 ≤ k ≤ 10 . In this paper, we improve the technique of the construction, by the use of the so-called projetive pseudo-metric, and we get non uniquely ergodic minimal (6, k)-IETs, \(1\le k\le 6\) 1 ≤ k ≤ 6 . Moreover, we introduce some general technical lemmas that will be useful to build new examples.