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<p>For (partially) analytic integrable differential systems near a periodic orbit <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation>, we demonstrate existence of a maximal dimensional submanifold including <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation> which is foliated by periodic orbits. In the case that <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\Gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation> is a trivial periodic orbit, i.e., a singular point, we provide a new criterion for the characterization of their isochronous centers when restricted to two dimensional systems.</p>

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Periodic Orbits of Partially Integrable Systems

  • 期刊论文

  • 发表日期：

    2025年10月24日

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  • Wenyong Huang,
  • Xiang Zhang

摘要

For (partially) analytic integrable differential systems near a periodic orbit \(\Gamma \) Γ , we demonstrate existence of a maximal dimensional submanifold including \(\Gamma \) Γ which is foliated by periodic orbits. In the case that \(\Gamma \) Γ is a trivial periodic orbit, i.e., a singular point, we provide a new criterion for the characterization of their isochronous centers when restricted to two dimensional systems.