具有幂零线性部分的平面向量场的返回映射：一个直接显式导子
The return map for a planar vector field with nilpotent linear part: a direct and explicit derivation
摘要：
用直接法证明了具有幂零线性部分的平面向量场焦点附近的返回映射是一个收敛的幂级数，它是恒等式的扰动，其项可以迭代计算.第一个非平凡系数是一个阿贝尔积分的值，下面的系数是显式给出的迭代积分。
英文摘要：
Using a direct approach the return map near a focus of a planar vector field with nilpotent linear part is found as a convergent power series which is a perturbation of the identity and whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
