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<p>In this paper we study the easiest polynomial differential systems in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12591_2025_737_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {R}}^4\)</EquationSource> </InlineEquation> exhibiting the invariant sphere <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12591_2025_737_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="157" /> </InlineMediaObject> <EquationSource Format="TEX">\(x^2+y^2+z^2+w^2=1\)</EquationSource> </InlineEquation>, and we describe the dynamics of the orbits on this invariant sphere.</p>

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The Easiest Polynomial Differential Systems in \({\mathbb {R}}^4\) Having an Invariant Sphere

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Jaume Llibre,
  • Renhao Tian

摘要

In this paper we study the easiest polynomial differential systems in \({\mathbb {R}}^4\) exhibiting the invariant sphere \(x^2+y^2+z^2+w^2=1\) , and we describe the dynamics of the orbits on this invariant sphere.