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<p>Carleman linearization is applied to a two-dimensional nonlinear system with a linear center. The solution of the Carleman-linearized system is obtained without relying on the Jordan canonical form for the matrix exponential, using Putzer’s method. The solution of the Carleman-linearized system evaluated at the first return time contains the Poincaré-Lyapunov constants. We introduce a constructive procedure to obtain these constants. Examples support the validity of the proposed method.</p>

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Carleman linearization of nonlinear systems with linear centers: return times and Poincaré-Lyapunov constants

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月3日

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  • Csanád Árpád Hubay,
  • Tamás Kalmár-Nagy

摘要

Carleman linearization is applied to a two-dimensional nonlinear system with a linear center. The solution of the Carleman-linearized system is obtained without relying on the Jordan canonical form for the matrix exponential, using Putzer’s method. The solution of the Carleman-linearized system evaluated at the first return time contains the Poincaré-Lyapunov constants. We introduce a constructive procedure to obtain these constants. Examples support the validity of the proposed method.