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<p>In this paper, we study the dynamics of geodesics of Fuchsian meromorphic connections with real periods, giving a precise characterization of the possible <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>-limit sets of simple geodesics in this case. The main tools are the study of the singular flat metric associated to the meromorphic connection, an explicit description of the geodesics nearby a Fuchsian pole with real residue larger than <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and a generalization to our case of the classical Teichmüller lemma for quadratic differentials.</p>

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Dynamics of Fuchsian meromorphic connections with real periods

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Marco Abate,
  • Karim Rakhimov

摘要

In this paper, we study the dynamics of geodesics of Fuchsian meromorphic connections with real periods, giving a precise characterization of the possible \(\omega \) ω -limit sets of simple geodesics in this case. The main tools are the study of the singular flat metric associated to the meromorphic connection, an explicit description of the geodesics nearby a Fuchsian pole with real residue larger than \(-1\) - 1 and a generalization to our case of the classical Teichmüller lemma for quadratic differentials.