Solutions non oscillantes d’une équation différentielle et corps de Hardy

Blais, François; Moussu, Robert; Sanz, Fernando

Blais, François ; Moussu, Robert ; Sanz, Fernando

Annales de l'Institut Fourier, Tome 57 (2007), p. 1825-1838 / Harvested from Numdam

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Résumé
Abstract

Soit $ϕ : x \mapsto ϕ (x), x ≫ 0$ une solution à l’infini d’une équation différentielle algébrique d’ordre $n$ , $P (x, y, y^{'}, ..., y^{(n)}) = 0$ . Nous donnons un critère géométrique pour que les germes à l’infini de $ϕ$ et de la fonction identité sur $ℝ$ appartiennent à un même corps de Hardy. Ce critère repose sur le concept de non oscillation.

Let $ϕ : x \mapsto ϕ (x), x ≫ 0$ be a solution of an algebraic differential equation of order $n$ , $P (x, y, y^{'}, ..., y^{(n)}) = 0$ . We establish a geometric criterion so that the germs at infinity of $ϕ$ and the identity function on $ℝ$ belong to a common Hardy field. This criterion is based on the concept of non oscillation.

Publié le : 2007-01-01

MR 2377887 | Zbl 1133.34007

DOI : https://doi.org/10.5802/aif.2314
Classification: 34A26, 34C10, 34C08, 37C10
Mots clés: oscillation, corps de Hardy, semi-algébrique, pfaffien

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     title = {Solutions non oscillantes d'une \'equation diff\'erentielle et corps de Hardy},
     journal = {Annales de l'Institut Fourier},
     volume = {57},
     year = {2007},
     pages = {1825-1838},
     doi = {10.5802/aif.2314},
     zbl = {1133.34007},
     mrnumber = {2377887},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_2007__57_6_1825_0}
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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) pp. 1825-1838. doi : 10.5802/aif.2314. http://gdmltest.u-ga.fr/item/AIF_2007__57_6_1825_0/

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