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<p>In this paper, we study the condition for the planar piecewise polynomial Hamiltonian system with separable variables (separated by <i>x</i>-axis) to have an isochronous center at the origin, and show that the origin is an isochronous center if and only if the two polynomial subsystems are both linear. This result generalizes the one by Liu and Wang (Proc Am Math Soc 150(6):2499–2507, 2022).</p>

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On the isochronous center of planar piecewise polynomial Hamiltonian system with separable variables

  • 期刊论文

  • 发表日期：

    2025年3月20日

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  • Zhaoxuan Huo,
  • Shaoqing Wang

摘要

In this paper, we study the condition for the planar piecewise polynomial Hamiltonian system with separable variables (separated by x-axis) to have an isochronous center at the origin, and show that the origin is an isochronous center if and only if the two polynomial subsystems are both linear. This result generalizes the one by Liu and Wang (Proc Am Math Soc 150(6):2499–2507, 2022).