Geodesic
Isomonodromy deformations of equations with irregular singularities
Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 463-479 
M. V. Fedoryuk. Isomonodromy deformations of equations with irregular singularities. Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 463-479. http://geodesic.mathdoc.fr/item/SM_1992_71_2_a12/
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     author = {M. V. Fedoryuk},
     title = {Isomonodromy deformations of equations with irregular singularities},
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     volume = {71},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1992_71_2_a12/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions are obtained for a deformation to be isomonodromic for higher-order systems and equations in a neighborhood of an irregular singular point in the case when all formal solutions are subnormal series. Examples are considered.

[1] Schlesinger L., “Zur Theorie der linearen Differentialgleichung in Anschless an des Riemannsche Problem”, Hourn. für Math., 193 (1912), 138

[2] Garnier R., “Sur les equations differentielles du troisieme ordre dont l'integrale generale est uniforme et sur une classe d'equations nouvelles d'ordre superieur dont l'integrale generale a ses points critiques fixes”, Ann. Scient. Ecole Norm. Sup., 29 (1912), 1–126 | MR | Zbl

[3] Ablovits M. Dzh., Segyur G., Solitony i obratnaya zadacha teorii rasseyaniya, Mir, M., 1985

[4] Its A. R., Novokshenov V. Yu., The isomonodromic deformation method in the theory of Painleve equations, Lecture Notes in Math., 1191, Springer, Berlin-Heidelberg-New York-Tokyo, 1986 | MR | Zbl

[5] Ueno K., “Monodromy preserving deformations of linear differential equations with irregular singular points”, Proc. Japan Acad. Ser. A, 1980, no. 8, 97–102 | DOI | MR | Zbl

[6] Ains E. L., Obyknovennye differentsialnye uravneniya, ONTI, Kharkov, 1939

[7] Fedoryuk M. V., Asimptoticheskie metody dlya lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1983 | MR | Zbl

[8] Sibuya Y., “Stokes phenomena”, Bull. Amer. Math. Soc., 83 (1977), 1075–1077 | DOI | MR | Zbl

[9] Balser W., “Solutions of first level of meromorphic differential equations”, Proc. of Edinburgh Math. Soc., 25 (1982), 183–207 | DOI | MR | Zbl

[10] Sato M., Dzimbo M., Miva T., Golonomnye kvantovye polya, Mir, M., 1983 | MR