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

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

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
\Bibitem{Gon04} \by R.~R.~Gontsov \paper Refined Fuchs inequalities for systems of linear differential equations \jour Izv. RAN. Ser. Mat. \yr 2004 \vol 68 \issue 2 \pages 39--52 \mathnet{http://mi.mathnet.ru/izv474} \crossref{https://doi.org/10.4213/im474} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2057999} \zmath{https://zbmath.org/?q=an:1078.34069} \transl \jour Izv. Math. \yr 2004 \vol 68 \issue 2 \pages 259--272 \crossref{https://doi.org/10.1070/IM2004v068n02ABEH000474} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000222755000003} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746531175} 

• http://mi.mathnet.ru/eng/izv474
• https://doi.org/10.4213/im474
• http://mi.mathnet.ru/eng/izv/v68/i2/p39

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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
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
3. Corel E., “Exponents of a meromorphic connection on a compact Riemann surface”, Pacific J. Math., 242:2 (2009), 259–279
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
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
6. Yu. P. Bibilo, “Isomonodromic deformations of systems of linear differential equations with irregular singularities”, Sb. Math., 203:6 (2012), 826–843
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