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<p>In this work we study a class of hybrid differential systems formed by two polynomial Hamiltonian systems separated by a straight line, which we named piecewise hybrid polynomial Hamiltonian systems. We investigate an upper bound for the maximum number of limit cycles that these piecewise hybrid polynomial Hamiltonian systems can exhibit when they have finitely many periodic solutions. Moreover we present some examples where this upper bound is reached. In other words we solve the extension of the 16th Hilbert problem to this class of hybrid differential systems.</p>

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Limit cycles for piecewise hybrid polynomial Hamiltonian differential systems

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • Camila A. B. Rodrigues de Lima,
  • Jaume Llibre

摘要

In this work we study a class of hybrid differential systems formed by two polynomial Hamiltonian systems separated by a straight line, which we named piecewise hybrid polynomial Hamiltonian systems. We investigate an upper bound for the maximum number of limit cycles that these piecewise hybrid polynomial Hamiltonian systems can exhibit when they have finitely many periodic solutions. Moreover we present some examples where this upper bound is reached. In other words we solve the extension of the 16th Hilbert problem to this class of hybrid differential systems.