具有中心或焦点的幂零线性部分的平面向量场的第一返回映射
The first return map for planar vector fields with nilpotent linear part with a center or a focus
摘要：
对于具有幂零线性部分的平面向量场（具有中心或焦点，并且在一般满足的假设下），其返回映射是一个收敛的幂级数，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，下面的系数是明确给出的代数函数建立的迭代积分。
英文摘要：
The return map for planar vector fields with nilpotent linear part (having a center or a focus and under an assumption generically satisfied) is found as a convergent power series 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 built with algebraic functions.
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。
