Differential Puiseux theorem in generalized series fields of finite rank

Mickael Matusinski (1)

1 Équipe Géométrie

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.

Domaines: Analyse classique [math.CA]

Mickael Matusinski. Differential Puiseux theorem in generalized series fields of finite rank. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2011, 20 (2), pp.247-293. ⟨10.5802/afst.1293⟩. ⟨hal-00946800⟩