有限秩广义级数域上的微分Puietrix定理
Differential Puiseux theorem in generalized series fields of finite rank
摘要：
本文研究了微分方程$F(y,...,y^{(n)})=0$，其中$F(Y_0,...,Y_n)$是$Y_0,...,Y_n$中的形式级数，系数在有限秩$r\in\mathbb{N}^*$的\emph{generalized power series} $\mathds{K}_r$的某个域上.我们的目的是理解方程$\textrm{Supp} F$的系数的指数集合和作为解的元素$y_0\in\mathds{K}_r$的指数集合$\textrm{Supp} y_0$之间的联系。
英文摘要：
We study differential equations $F(y,...,y^{(n)})=0$ where $F(Y_0,...,Y_n)$ is a formal series in $Y_0,...,Y_n$ with coefficients in some field of \emph{generalized power series} $\mathds{K}_r$ with finite rank $r\in\mathbb{N}^*$. Our purpose is to understand the connection between the set of exponents of the coefficients of the equation $\textrm{Supp} F$ and the set $\textrm{Supp} y_0$ of exponents of the elements $y_0\in\mathds{K}_r$ that are solutions.
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。
