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arXiv · 0902.1758

Differential Puiseux theorem in generalized series fields of finite rank

Mickael Matusinski
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Abstract

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.

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Mickael Matusinski. 2009-02-10. Differential Puiseux theorem in generalized series fields of finite rank. https://arxiv.org/abs/0902.1758

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