三次多项式系统的弱持久中心和等时中心问题的完整解
Complete solution to the weak persistent center and isochronous center problems of cubic polynomial systems
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中文总结 AI 辅助
本文通过奇点量与拟李雅普诺夫常数方法，完整求解了三次多项式系统弱持久中心及等时中心问题，给出了复与实系统的充要条件。
中文摘要 AI 辅助
本文研究了几类平面三次微分系统的弱持久中心，包括具有非退化线性中心的系统和具有幂零中心的系统。通过计算奇点量或拟李雅普诺夫常数，获得了必要的参数关系，并通过适当的解析构造建立了其充分性。对于一般复三次系统，我们得到了原点为弱持久中心的充分必要条件，相应的实三次系统的结果通过对复系数施加共轭关系而得出。我们进一步结合弱持久中心条件与线性化量的消失，并构造保时的解析线性化，刻画了一般复三次系统的弱持久等时中心。
英文摘要
In this paper, we investigate weakly persistent centers for several classes of planar cubic differential systems, including systems with a nondegenerate linear center and systems with a nilpotent center. Necessary parameter relations are obtained by computing singular point quantities or quasi-Lyapunov constants, while their sufficiency is established by suitable analytic constructions. For the general complex cubic system, we obtain necessary and sufficient conditions for the origin to be a weakly persistent center, and the corresponding result for the associated general real cubic system follows by imposing the conjugacy relations between the complex coefficients. We further characterize the weakly persistent isochronous centers of the general complex cubic system by combining the weakly persistent center conditions with the vanishing of the linearization quantities and constructing time-preserving analytic linearizations.
发表机构
- Linyi University（临沂大学）
- Shanghai Jiao Tong University（上海交通大学）
- Western University（韦仕敦大学）
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