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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 5, Pages 1084–1109 (Mi izv1881)  

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


Abstract: 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.
Bibliography: 4 titles.

Full text: PDF file (2141 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:5, 1031–1054

Bibliographic databases:

UDC: 517.9
MSC: Primary 34A30, 34A20; Secondary 34C05, 33A30
Received: 14.07.1975

Citation: 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
\Bibitem{Bol77}
\by A.~A.~Bolibrukh
\paper On the fundamental matrix of a~Pfaffian system of Fuchsian type
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 5
\pages 1084--1109
\mathnet{http://mi.mathnet.ru/izv1881}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=501056}
\zmath{https://zbmath.org/?q=an:0414.35019|0424.35024}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 5
\pages 1031--1054
\crossref{https://doi.org/10.1070/IM1977v011n05ABEH001757}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  zmath  isi
    2. V. A. Golubeva, “On systems with regular singularities, and their solutions”, Math. USSR-Izv., 27:1 (1986), 27–38  mathnet  crossref  mathscinet  zmath
    3. A. A. Bolibrukh, “The Riemann–Hilbert problem”, Russian Math. Surveys, 45:2 (1990), 1–58  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. V. A. Golubeva, V. P. Leksin, “Generalized Knizhnik–Zamolodchikov equations and the factorization of their solutions”, Math. Notes, 54:5 (1993), 1100–1105  mathnet  crossref  mathscinet  zmath  isi  elib
    5. A. A. Bolibruch, “On isomonodromic deformations of Fuchsian systems”, J Dyn Control Syst, 3:4 (1997), 589  crossref  mathscinet  zmath  elib
    6. 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  mathnet  mathscinet  zmath
    7. D. V. Anosov, V. I. Arnol'd, V. M. Buchstaber, V. A. Golubeva, A. A. Gonchar, A. B. Zhizhchenko, Yu. S. Ilyashenko, V. V. Kozlov, S. P. Konovalov, L. D. Kudryavtsev, V. P. Leksin, O. B. Lupanov, A. A. Mal'tsev, E. F. Mishchenko, S. P. Novikov, Yu. S. Osipov, M. M. Postnikov, V. A. Sadovnichii, A. G. Sergeev, L. D. Faddeev, A. V. Chernavskii, “Andrei Andreevich Bolibrukh (obituary)”, Russian Math. Surveys, 58:6 (2003), 1185–1189  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    8. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    9. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Davide Guzzetti, “Notes on Non-Generic Isomonodromy Deformations”, SIGMA, 14 (2018), 087, 34 pp.  mathnet  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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