Geodesic
Some properties of Malgrange isomonodromic deformations of linear $2\times2$ systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical control theory and differential equations, Tome 277 (2012), pp. 22-32.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study movable singularities of the Malgrange isomonodromic deformation of a linear differential $2\times 2$ system with two irregular singularities of Poincaré rank $1$ and with an arbitrary number of Fuchsian singular points. 
@article{TM_2012_277_a1,
     author = {Yu. P. Bibilo and R. R. Gontsov},
     title = {Some properties of {Malgrange} isomonodromic deformations of linear $2\times2$ systems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {22--32},
     publisher = {mathdoc},
     volume = {277},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_277_a1/}
}
TY  - JOUR
AU  - Yu. P. Bibilo
AU  - R. R. Gontsov
TI  - Some properties of Malgrange isomonodromic deformations of linear $2\times2$ systems
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2012
SP  - 22
EP  - 32
VL  - 277
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2012_277_a1/
LA  - ru
ID  - TM_2012_277_a1
ER  - 
%0 Journal Article
%A Yu. P. Bibilo
%A R. R. Gontsov
%T Some properties of Malgrange isomonodromic deformations of linear $2\times2$ systems
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2012
%P 22-32
%V 277
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2012_277_a1/
%G ru
%F TM_2012_277_a1
Yu. P. Bibilo; R. R. Gontsov. Some properties of Malgrange isomonodromic deformations of linear $2\times2$ systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical control theory and differential equations, Tome 277 (2012), pp. 22-32. http://geodesic.mathdoc.fr/item/TM_2012_277_a1/

[1] Bolibrukh A.A., “O tau-funktsii uravneniya izomonodromnykh deformatsii Shlezingera”, Mat. zametki, 74:2 (2003), 184–191 | DOI | MR | Zbl

[2] Bolibruch A.A., “On orders of movable poles of the Schlesinger equation”, J. Dyn. Control Syst., 6:1 (2000), 57–73 | DOI | MR | Zbl

[3] Bolibruch A.A., “On isomonodromic deformations of Fuchsian systems”, J. Dyn. Control Syst., 3:4 (1997), 589–604 | MR | Zbl

[4] Bolibrukh A.A., Obratnye zadachi monodromii v analiticheskoi teorii differentsialnykh uravnenii, MTsNMO, M., 2009

[5] Bolibruch A.A., Malek S., Mitschi C., “On the generalized Riemann–Hilbert problem with irregular singularities”, Expo. Math., 24:3 (2006), 235–272 | DOI | MR | Zbl

[6] Vyugin I.V., Gontsov R.R., “O dopolnitelnykh parametrakh v obratnykh zadachakh monodromii”, Mat. sb., 197:12 (2006), 43–64 | DOI | MR | Zbl

[7] Gontsov R.R., Vyugin I.V., “Apparent singularities of Fuchsian equations and the Painlevé property for Garnier systems”, J. Geom. Phys., 61:12 (2011), 2419–2435 | DOI | MR | Zbl

[8] Deligne P., Equations différentielles à points singuliers réguliers, Lect. Notes Math., 163, Springer, Berlin, 1970 | MR | Zbl

[9] Ilyashenko Yu., Yakovenko S., Lectures on analytic differential equations, Grad. Stud. Math., 86, Amer. Math. Soc., Providence, RI, 2008 | MR | Zbl

[10] Its A.R., Kapaev A.A., Novokshenov V.Yu., Fokas A.S., Transtsendenty Penleve. Metod zadachi Rimana, Regulyarnaya i khaoticheskaya dinamika, Moskva; Izhevsk, 2005

[11] Levelt A., “Hypergeometric functions. II”, Nederl. Acad. Wet. Proc. A, 64 (1961), 373–385 | MR | Zbl

[12] Malgrange B., “Sur les déformations isomonodromiques. II: Singularités irrégulières”, Mathématique et physique: Sémin. Ec. Norm. Supér. (Paris, 1979–1982), Progr. Math., 37, Birkhäuser, Boston, 1983, 427–438 | MR

[13] Malgrange B., “Connexions méromorphes. II: Le réseau canonique”, Invent. math., 124 (1996), 367–387 | DOI | MR | Zbl

[14] Palmer J., “Zeros of the Jimbo, Miwa, Ueno tau function”, J. Math. Phys., 40:12 (1999), 6638–6681 | DOI | MR | Zbl

[15] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR

[16] Schlesinger L., “Über die Lösungen gewisser linearer Differentialgleichungen als Funktionen der singulären Punkte”, J. reine angew. Math., 129 (1905), 287–294

[17] Schlesinger L., “Über eine Klasse von Differentialsystemen beliebiger Ordnung mit festen kritischen Punkten”, J. reine angew. Math., 141 (1912), 96–145 | Zbl