A differential Puiseux theorem in generalized series fields of finite rank
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 2, pp. 247-293.

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 * . Our purpose is to express the support Suppy 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 SuppF.

Nous étudions des équations différentielles F(y,...,y (n) )=0F est une séries formelle en y,y ,...,y (n) , à coefficients dans un corps de séries généralisées 𝕂 r de rang fini r * . Notre objet est d’exprimer le support – c’est-à-dire l’ensemble Suppy 0 des exposants – des éléments y 0 𝕂 r solutions, en fonction des supports des coefficients de l’équation, dont l’union est notée SuppF.

DOI: 10.5802/afst.1293
Matusinski, Mickaël 1

1 Universität Konstanz, Fachbereich Mathematik und Statistik, 78457 Konstanz, Allemagne.
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     title = {A differential {Puiseux} theorem in generalized series fields of finite rank},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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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, Serie 6, Volume 20 (2011) no. 2, pp. 247-293. doi : 10.5802/afst.1293. http://www.numdam.org/articles/10.5802/afst.1293/

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