Comptes Rendus
no. 9
Ordinary differential equations
Uniform simplification in a full neighborhood of a turning point
[Simplification uniforme au voisinage d'un point tournant]

Présenté par : Jean-Pierre Ramis

Charlotte Hulek1
1 IRMA, UMR 7501, 7, rue René-Descartes, 67084 Strasbourg cedex, France
Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 789-793.

Nous donnons une version analytique d'un théorème formel dû à R.J. Hanson et D.L. Russell. Il s'agit d'un résultat de simplification uniforme au voisinage d'un point tournant pour des équations différentielles linéaires singulièrement perturbées du second ordre, qui généralise un théorème connu de Y. Sibuya.

We give an analytic version of a formal theorem due to R.J. Hanson and D.L. Russell. This version is a result of uniform simplification in a full neighborhood of a turning point for linear singularly perturbed differential equations of the second order, which generalizes a well-known theorem of Y. Sibuya.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.06.011
Charlotte Hulek 1

1 IRMA, UMR 7501, 7, rue René-Descartes, 67084 Strasbourg cedex, France 
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Charlotte Hulek. Uniform simplification in a full neighborhood of a turning point. Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 789-793. doi : 10.1016/j.crma.2015.06.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.06.011/

[1] A. Fruchard; R. Schäfke Composite asymptotic expansions and turning points of singularly perturbed ordinary differential equations, C. R. Acad. Sci. Paris, Ser. I, Volume 348 (2010) no. 23–24, pp. 1273-1277

[2] A. Fruchard; R. Schäfke Composite Asymptotic Expansions, Lecture Notes in Mathematics, vol. 2066, Springer, 2013

[3] R.J. Hanson; D.L. Russell Classification and reduction of second-order systems at a turning point, J. Math. Phys., Volume 46 (1967), pp. 74-92

[4] C. Hulek Classification and reduction of second-order systems at a turning point, Dyn. Syst. (2014) (Université de Strasbourg, France)

[5] F.W. Schäfke; R. Schäfke Zur Parameterabhängigkeit bei Differentialgleichungen, J. Reine Angew. Math., Volume 361 (1985), pp. 1-10

[6] Y. Sibuya Uniform simplification in a full neighborhood of a transition point, Mem. Amer. Math. Soc., Volume 149 (1974)

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