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<p>This paper investigates the limit cycle problem for a class of cubic isochronous Hamiltonian systems, when they are perturbed inside of polynomials of degree <i>n</i>. A upper bound of the number of limit cycles is obtained using the Abelian integral. Moreover, this bound is sharp. The method for obtaining the algebraic structure of the Abelian integral differs from those in other literature.</p>

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The Exact Number of Limit Cycles in a Class of Cubic Isochronous Hamiltonian Systems

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Jihua Yang,
  • Qipeng Zhang

摘要

This paper investigates the limit cycle problem for a class of cubic isochronous Hamiltonian systems, when they are perturbed inside of polynomials of degree n. A upper bound of the number of limit cycles is obtained using the Abelian integral. Moreover, this bound is sharp. The method for obtaining the algebraic structure of the Abelian integral differs from those in other literature.