This article is cited in 8 scientific papers (total in 10 papers)
On the fundamental matrix of a Pfaffian system of Fuchsian type
A. A. Bolibrukh
A necessary and sufficient condition is given in order that a completely integrable Pfaffian system with regular singular point, given on a polydisk $D^n$, be of Fuchsian type. It is proved that the system is Fuchsian if and only if the space of solutions is “weakly singular”. In the one-dimensional case, this problem was studied by A. H. M. Levelt (RZhMat., 1963, 12B56). For higher dimensions, a similar attempt was made by R. Gérard (RZhMat., 1970, IA553), but his paper contains an error.
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Mathematics of the USSR-Izvestiya, 1977, 11:5, 1031–1054
MSC: Primary 34A30, 34A20; Secondary 34C05, 33A30
A. A. Bolibrukh, “On the fundamental matrix of a Pfaffian system of Fuchsian type”, Izv. Akad. Nauk SSSR Ser. Mat., 41:5 (1977), 1084–1109; Math. USSR-Izv., 11:5 (1977), 1031–1054
Citation in format AMSBIB
\paper On the fundamental matrix of a~Pfaffian system of Fuchsian type
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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V. A. Golubeva, “On the recovery of a Pfaffian system of Fuchsian type from the generators of the monodromy group”, Math. USSR-Izv., 17:2 (1981), 227–241
V. A. Golubeva, “On systems with regular singularities, and their solutions”, Math. USSR-Izv., 27:1 (1986), 27–38
A. A. Bolibrukh, “The Riemann–Hilbert problem”, Russian Math. Surveys, 45:2 (1990), 1–58
V. A. Golubeva, V. P. Leksin, “Generalized Knizhnik–Zamolodchikov equations and the factorization of their solutions”, Math. Notes, 54:5 (1993), 1100–1105
A. A. Bolibruch, “On isomonodromic deformations of Fuchsian systems”, J Dyn Control Syst, 3:4 (1997), 589
V. A. Golubeva, V. P. Leksin, “Algebraic Characterization of the Monodromy of Generalized Knizhnik–Zamolodchikov Equations of $B_n$ Type”, Proc. Steklov Inst. Math., 238 (2002), 115–133
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D. V. Anosov, V. P. Leksin, “Andrei Andreevich Bolibrukh in life and science (30 January 1950 – 11 November 2003)”, Russian Math. Surveys, 59:6 (2004), 1009–1028
D. V. Anosov, V. P. Leksin, “Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations”, Russian Math. Surveys, 66:1 (2011), 1–33
Davide Guzzetti, “Notes on Non-Generic Isomonodromy Deformations”, SIGMA, 14 (2018), 087, 34 pp.
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