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<p>In this paper, we solve the Center-Focus Problem for a class of polynomial vector fields in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb {R}}^3\)</EquationSource> </InlineEquation> that have a singular point of Hopf type and whose center manifold at this point is an invariant sphere.</p>

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Center-Focus Problem on Invariant Spheres of 3D Quadratic Vector Fields

  • 期刊论文

  • 发表日期：

    2026年4月22日

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  • Márcio Gouveia,
  • Claudio Pessoa,
  • Weber F. Pereira

摘要

In this paper, we solve the Center-Focus Problem for a class of polynomial vector fields in the \({\mathbb {R}}^3\) that have a singular point of Hopf type and whose center manifold at this point is an invariant sphere.