We study differential equations where is a formal series in with coefficients in some field of generalized power series with finite rank . Our purpose is to express the support , i.e. the set of exponents, of the elements that are solutions, in terms of the supports of the coefficients of the equation, namely .
Nous étudions des équations différentielles où est une séries formelle en , à coefficients dans un corps de séries généralisées de rang fini . Notre objet est d’exprimer le support – c’est-à-dire l’ensemble des exposants – des éléments solutions, en fonction des supports des coefficients de l’équation, dont l’union est notée .
@article{AFST_2011_6_20_2_247_0, author = {Matusinski, Micka\"el}, title = {A differential {Puiseux} theorem in generalized series fields of finite rank}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {247--293}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 20}, number = {2}, year = {2011}, doi = {10.5802/afst.1293}, zbl = {1222.34012}, mrnumber = {2847885}, language = {en}, url = {http://www.numdam.org/articles/10.5802/afst.1293/} }
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 PY - 2011 SP - 247 EP - 293 VL - 20 IS - 2 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1293/ DO - 10.5802/afst.1293 LA - en ID - AFST_2011_6_20_2_247_0 ER -
%0 Journal Article %A Matusinski, Mickaël %T A differential Puiseux theorem in generalized series fields of finite rank %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2011 %P 247-293 %V 20 %N 2 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://www.numdam.org/articles/10.5802/afst.1293/ %R 10.5802/afst.1293 %G en %F AFST_2011_6_20_2_247_0
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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