A differential Puiseux theorem in generalized series fields of finite rank

Mickaël Matusinski[1]

  • [1] Universität Konstanz, Fachbereich Mathematik und Statistik, 78457 Konstanz, Allemagne.

Annales de la faculté des sciences de Toulouse Mathématiques (2011)

  • Volume: 20, Issue: 2, page 247-293
  • ISSN: 0240-2963

Abstract

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We study differential equations F ( y , ... , y ( n ) ) = 0 where F is a formal series in y , y ′ , ... , y ( n ) with coefficients in some field of generalized power series 𝕂 r with finite rank r ∈ ℕ * . Our purpose is to express the support Supp y 0 , i.e. the set of exponents, of the elements y 0 ∈ 𝕂 r that are solutions, in terms of the supports of the coefficients of the equation, namely Supp F .

How to cite

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Matusinski, Mickaël. "A differential Puiseux theorem in generalized series fields of finite rank." Annales de la faculté des sciences de Toulouse Mathématiques 20.2 (2011): 247-293. <http://eudml.org/doc/219705>.

@article{Matusinski2011,
abstract = {We study differential equations $F(y,\ldots ,y^\{(n)\})=0$ where $F$ is a formal series in $y,y^\{\prime\},\ldots ,y^\{(n)\}$ with coefficients in some field of generalized power series$\{\mathbb\{K\}\}_r$ with finite rank $r\in \{\mathbb\{N\}\}^*$. Our purpose is to express the support $\textrm\{Supp\}\ y_0$, i.e. the set of exponents, of the elements $y_0\in \{\mathbb\{K\}\}_r$ that are solutions, in terms of the supports of the coefficients of the equation, namely $\textrm\{Supp\}\ F$.},
affiliation = {Universität Konstanz, Fachbereich Mathematik und Statistik, 78457 Konstanz, Allemagne.},
author = {Matusinski, Mickaël},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {differential Puiseux theorem; generalized series fields; finite rank},
language = {eng},
month = {4},
number = {2},
pages = {247-293},
publisher = {Université Paul Sabatier, Toulouse},
title = {A differential Puiseux theorem in generalized series fields of finite rank},
url = {http://eudml.org/doc/219705},
volume = {20},
year = {2011},
}

TY - JOUR
AU - Matusinski, Mickaël
TI - A differential Puiseux theorem in generalized series fields of finite rank
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2011/4//
PB - Université Paul Sabatier, Toulouse
VL - 20
IS - 2
SP - 247
EP - 293
AB - We study differential equations $F(y,\ldots ,y^{(n)})=0$ where $F$ is a formal series in $y,y^{\prime},\ldots ,y^{(n)}$ with coefficients in some field of generalized power series${\mathbb{K}}_r$ with finite rank $r\in {\mathbb{N}}^*$. Our purpose is to express the support $\textrm{Supp}\ y_0$, i.e. the set of exponents, of the elements $y_0\in {\mathbb{K}}_r$ that are solutions, in terms of the supports of the coefficients of the equation, namely $\textrm{Supp}\ F$.
LA - eng
KW - differential Puiseux theorem; generalized series fields; finite rank
UR - http://eudml.org/doc/219705
ER -

References

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