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<p>We establish that the asymptotic mean action and the asymptotic linking number of irrational pseudo-rotations remain well-defined everywhere and constant for every <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^{1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> irrational pseudo-rotation that behaves as a rotation on the boundary. As a consequence, we demonstrate that the isotopy of irrational pseudo-rotations with a positive rotation number is a right-handed isotopy in the sense of Ghys.</p>

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The asymptotic mean action and the asymptotic linking number for pseudo-rotations

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • David Bechara Senior,
  • Patrice Le Calvez,
  • Abror Pirnapasov

摘要

We establish that the asymptotic mean action and the asymptotic linking number of irrational pseudo-rotations remain well-defined everywhere and constant for every \(C^{1}\) C 1 irrational pseudo-rotation that behaves as a rotation on the boundary. As a consequence, we demonstrate that the isotopy of irrational pseudo-rotations with a positive rotation number is a right-handed isotopy in the sense of Ghys.