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This chapter examines the generic geometric deformations of the butterfly, goose, and gull singularities in two-parameter families of map-germs from the plane to the plane. Explicit descriptions are provided for how singularities, inflections, and vertices emerge, split, or disappear as the parameters vary. For the butterfly singularity, the generic geometric deformations correspond to its \(\mathcal A\) -versal deformations. The goose singularity possesses two distinct generic geometric deformations, whereas the gull singularities possess twelve.

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Geometric Deformations of \(\mathcal A_e\) -codimension 2 Singularities

  • 章节

  • 发表日期：

    2025年

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  • Farid Tari,
  • Mostafa Salarinoghabi,
  • Masaru Hasegawa

摘要

This chapter examines the generic geometric deformations of the butterfly, goose, and gull singularities in two-parameter families of map-germs from the plane to the plane. Explicit descriptions are provided for how singularities, inflections, and vertices emerge, split, or disappear as the parameters vary. For the butterfly singularity, the generic geometric deformations correspond to its \(\mathcal A\) -versal deformations. The goose singularity possesses two distinct generic geometric deformations, whereas the gull singularities possess twelve.