AI 中文总结
本文研究由两个外圆分隔的三区域分片全纯系统扰动线性中心时极限环的分支数量，并证明在特定构型下四次系统至少存在十六个极限环。
AI 中文摘要
本文研究了当线性中心的周期轨道受到由两个外圆分隔的三区域分片全纯系统扰动时，从这些周期轨道分支出的极限环数量。我们分析了这些区域的不同几何构型如何影响极限环的数量。此外，我们证明了在特定构型下，四次分片多项式全纯系统中至少存在十六个极限环。
英文摘要
This work investigates the number of limit cycles bifurcating from the periodic orbits of a linear center when it is perturbed by piecewise holomorphic systems with three zones separated by two external circles. We analyze how different geometric configurations of these zones influence the number of limit cycles. Moreover, we show the existence of at least sixteen limit cycles in fourth-degree piecewise polynomial holomorphic systems under certain configurations.
