Let be a solution of an algebraic differential equation of order , . We establish a geometric criterion so that the germs at infinity of and the identity function on belong to a common Hardy field. This criterion is based on the concept of non oscillation.
Soit une solution à l’infini d’une équation différentielle algébrique d’ordre , . Nous donnons un critère géométrique pour que les germes à l’infini de et de la fonction identité sur appartiennent à un même corps de Hardy. Ce critère repose sur le concept de non oscillation.
Mot clés : oscillation, corps de Hardy, semi-algébrique, pfaffien
Keywords: oscillation, Hardy field, semi-algebraic, pfaffian
@article{AIF_2007__57_6_1825_0, author = {Blais, Fran\c{c}ois and Moussu, Robert and Sanz, Fernando}, title = {Solutions non oscillantes d{\textquoteright}une \'equation diff\'erentielle et corps de {Hardy}}, journal = {Annales de l'Institut Fourier}, pages = {1825--1838}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {57}, number = {6}, year = {2007}, doi = {10.5802/aif.2314}, zbl = {1133.34007}, mrnumber = {2377887}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/aif.2314/} }
TY - JOUR AU - Blais, François AU - Moussu, Robert AU - Sanz, Fernando TI - Solutions non oscillantes d’une équation différentielle et corps de Hardy JO - Annales de l'Institut Fourier PY - 2007 SP - 1825 EP - 1838 VL - 57 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2314/ DO - 10.5802/aif.2314 LA - fr ID - AIF_2007__57_6_1825_0 ER -
%0 Journal Article %A Blais, François %A Moussu, Robert %A Sanz, Fernando %T Solutions non oscillantes d’une équation différentielle et corps de Hardy %J Annales de l'Institut Fourier %D 2007 %P 1825-1838 %V 57 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2314/ %R 10.5802/aif.2314 %G fr %F AIF_2007__57_6_1825_0
Blais, François; Moussu, Robert; Sanz, Fernando. Solutions non oscillantes d’une équation différentielle et corps de Hardy. Annales de l'Institut Fourier, Volume 57 (2007) no. 6, pp. 1825-1838. doi : 10.5802/aif.2314. http://archive.numdam.org/articles/10.5802/aif.2314/
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