Invariants mesurant l'irrégularité en un point singulier des systèmes d'équations différentielles linéaires
Annales de l'Institut Fourier, Volume 23 (1973) no. 1, p. 157-195

We define integer invariants measuring the irregularity near a singular point of a differential system. The properties of these invariants together with the study of the variation of the order of the singularity by linear perturbations and a generalization of a result of W. Jurkat and D.A. Lutz, allows us to give an algebraic way to determine the order of the singularity.

On définit des invariants entiers mesurant l’irrégularité d’un point singulier d’un système différentiel. Les propriétés de ces invariants, l’étude de la variation de l’ordre de la singularité par perturbation linéaire ainsi qu’une généralisation d’un théorème de W. Jurkat et D.A. Lutz permettent de donner une méthode de calcul de cet ordre.

@article{AIF_1973__23_1_157_0,
     author = {G\'erard, R. and Levelt, A. M.},
     title = {Invariants mesurant l'irr\'egularit\'e en un point singulier des syst\`emes d'\'equations diff\'erentielles lin\'eaires},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {23},
     number = {1},
     year = {1973},
     pages = {157-195},
     doi = {10.5802/aif.449},
     zbl = {0243.35016},
     mrnumber = {49 \#10947},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1973__23_1_157_0}
}
Gérard, R.; Levelt, A. M. Invariants mesurant l'irrégularité en un point singulier des systèmes d'équations différentielles linéaires. Annales de l'Institut Fourier, Volume 23 (1973) no. 1, pp. 157-195. doi : 10.5802/aif.449. http://www.numdam.org/item/AIF_1973__23_1_157_0/

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