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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 2, Pages 39–52 (Mi izv474)  

This article is cited in 6 scientific papers (total in 6 papers)

Refined Fuchs inequalities for systems of linear differential equations

R. R. Gontsov


Abstract: We refine the Fuchs inequalities obtained by Corel for systems of linear meromorphic differential equations given on the Riemann sphere. Fuchs inequalities enable one to estimate the sum of exponents of the system over all its singular points. We refine these well-known inequalities by considering the Jordan structure of the leading coefficient of the Laurent series for the matrix of the right-hand side of the system in the neighbourhood of a singular point.

DOI: https://doi.org/10.4213/im474

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English version:
Izvestiya: Mathematics, 2004, 68:2, 259–272

Bibliographic databases:

UDC: 517.531.57
MSC: 34-02, 34M99, 34M50, 34A30
Received: 11.09.2003

Citation: R. R. Gontsov, “Refined Fuchs inequalities for systems of linear differential equations”, Izv. RAN. Ser. Mat., 68:2 (2004), 39–52; Izv. Math., 68:2 (2004), 259–272

Citation in format AMSBIB
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\paper Refined Fuchs inequalities for systems of linear differential equations
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\vol 68
\issue 2
\pages 39--52
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\pages 259--272
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    Erratum

    This publication is cited in the following articles:
    1. R. R. Gontsov, “Letter to the editors”, Izv. Math., 68:6 (2004), 1277–1279  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. R. R. Gontsov, “Orders of Zeros of Polynomials on Trajectories of Solutions of a System of Linear Differential Equations with Regular Singular Points”, Math. Notes, 76:3 (2004), 438–442  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Corel E., “Exponents of a meromorphic connection on a compact Riemann surface”, Pacific J. Math., 242:2 (2009), 259–279  crossref  mathscinet  zmath  isi  elib  scopus
    4. I. V. V'yugin, R. R. Gontsov, “Construction of a system of linear differential equations from a scalar equation”, Proc. Steklov Inst. Math., 271 (2010), 322–338  mathnet  crossref  mathscinet  isi  elib
    5. 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
    6. Yu. P. Bibilo, “Isomonodromic deformations of systems of linear differential equations with irregular singularities”, Sb. Math., 203:6 (2012), 826–843  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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