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.
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.
Classification : 34A26, 34C10, 34C08, 37C10
Mots clés : oscillation, corps de Hardy, semi-algébrique, pfaffien
@article{AIF_2007__57_6_1825_0, author = {Blais, Fran\c cois and Moussu, Robert and Sanz, Fernando}, title = {Solutions non oscillantes d'une \'equation diff\'erentielle et corps de Hardy}, journal = {Annales de l'Institut Fourier}, pages = {1825--1838}, publisher = {Association des Annales de l'institut Fourier}, volume = {57}, number = {6}, year = {2007}, doi = {10.5802/aif.2314}, mrnumber = {2377887}, zbl = {1133.34007}, language = {fr}, url = {archive.numdam.org/item/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, Tome 57 (2007) no. 6, pp. 1825-1838. doi : 10.5802/aif.2314. http://archive.numdam.org/item/AIF_2007__57_6_1825_0/
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