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<p>We analyze the polynomial vector fields in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^3\)</EquationSource> </InlineEquation> that have the Whitney umbrella as an invariant surface. We characterize the maximum number of invariant meridians and parallels that such polynomial vector fields in the Whitney umbrella can have in function of the degree of the polynomial vector field. Some algebraic computations have been done with the algebraic manipulator Mathematica.</p>

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Polynomial Vector Fields on the Whitney Umbrella

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • Jaume Llibre,
  • Adrian C. Murza

摘要

We analyze the polynomial vector fields in \(\mathbb {R}^3\) that have the Whitney umbrella as an invariant surface. We characterize the maximum number of invariant meridians and parallels that such polynomial vector fields in the Whitney umbrella can have in function of the degree of the polynomial vector field. Some algebraic computations have been done with the algebraic manipulator Mathematica.