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<p>We show that binary differential equations with coefficients vanishing at a point are locally topologically determined by their multiplicities when their discriminant has a Morse singularity. We also prove a similar result for a specific case where the singularity is more degenerate than Morse.</p>

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On the Topological Determinacy of Certain Binary Differential Equations

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Fabio Scalco Dias,
  • Luis Fernando Mello,
  • Farid Tari

摘要

We show that binary differential equations with coefficients vanishing at a point are locally topologically determined by their multiplicities when their discriminant has a Morse singularity. We also prove a similar result for a specific case where the singularity is more degenerate than Morse.