Differential Equations

, Volume 54, Issue 1, pp 1–6 | Cite as

Construction of a Fuchs Equation with Four Given Finite Singular Points and Given Reducible 2 × 2 Monodromy Matrices

Ordinary Differential Equations

Abstract

On the complex projective line, we construct a Fuchs equation with four given finite singular points and with fundamental solution matrix that has given reducible 2×2 monodromy matrices in the nonresonance case.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bolibrukh, A.A., The Riemann–Hilbert problem, Russ. Math. Surveys, 1990, vol. 45, no. 2, pp. 1–58.MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bolibrukh, A.A., Differential equations with meromorphic coefficients, in Contemporary Problems of Mathematics, Moscow: Mat. Inst. Steklova, 2003, vol. 1, pp. 29–82.MathSciNetMATHGoogle Scholar
  3. 3.
    Dekkers, W., The matrix of a connection having regular singularities on a vector bundle of rank 2 on P1(C), Lect. Notes Math, 1979, vol. 712, pp. 33–43.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Amel’kin, V.V. and Vasilevich, M.N., Construction of the Fuchs equation with four finite singular points and a given reducible monodromy group, Vestsi Akad. Navuk Belarusi, Ser. Fiz.-Mat. Navuk, 2014, no. 4, pp. 25–31.Google Scholar
  5. 5.
    Erugin, N.P., Riemann’s problem. II, Differ. Uravn., 1976, vol. 12, no. 5, pp. 779–799.MathSciNetMATHGoogle Scholar
  6. 6.
    Lappo-Danilevskii, I.A., Primenenie funktsii ot matrits k teorii lineinykh sistem obyknovennykh differentsial’nykh uravnenii (Application of Functions ofMatrices to the Theory of Linear Systems of Ordinary Differential Equations), Moscow: Gos. Izd. Tekh. Teor. Lit., 1957.Google Scholar
  7. 7.
    Amel’kin, V.V., Differentsial’nye uravneniya s mnogomernym vremenem: Avtonomnye i lineinye uravneniya (Differential Equations with “Multidimensional Time”: Autonomous and Linear Equations), Saarbrücken: Lambert Academic, 2012.Google Scholar
  8. 8.
    Erugin, N.P., Riemann’s problem. I, Differ. Uravn., 1975, vol. 11, no. 5, pp. 771–781.MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Belarusian State UniversityMinskBelarus

Personalised recommendations