常微分方程中心问题的Shuffle和Faà di Bruno霍普夫代数
Shuffle and Faà di Bruno Hopf Algebras in the Center Problem for Ordinary Differential Equations
摘要：
本文讨论了微分方程$\frac{dv}{dx}=\sum_{i=1}^{\infty}a_{i}(x)v^{i+1}$，$x\in [0,T]$中心问题的霍普夫代数方法，并研究了该方程第一返回映射的一些组合性质.本文总结和扩展了以前开发的方法，由于Devlin和作者的中心问题。
英文摘要：
In this paper we describe the Hopf algebra approach to the center problem for the differential equation $\frac{dv}{dx}=\sum_{i=1}^{\infty}a_{i}(x)v^{i+1}$, $x\in [0,T]$, and study some combinatorial properties of the first return map of this equation. The paper summarizes and extends previously developed approaches to the center problem due to Devlin and the author.
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。
