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

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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.

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References

  1. Bolibrukh, A.A., The Riemann–Hilbert problem, Russ. Math. Surveys, 1990, vol. 45, no. 2, pp. 1–58.

    Article  MathSciNet  MATH  Google Scholar 

  2. Bolibrukh, A.A., Differential equations with meromorphic coefficients, in Contemporary Problems of Mathematics, Moscow: Mat. Inst. Steklova, 2003, vol. 1, pp. 29–82.

    MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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. Erugin, N.P., Riemann’s problem. II, Differ. Uravn., 1976, vol. 12, no. 5, pp. 779–799.

    MathSciNet  MATH  Google Scholar 

  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. 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. Erugin, N.P., Riemann’s problem. I, Differ. Uravn., 1975, vol. 11, no. 5, pp. 771–781.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Belarusian State University, Minsk, 220030, Belarus

    V. V. Amel’kin & M. N. Vasilevich

Authors
  1. V. V. Amel’kin
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  2. M. N. Vasilevich
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Correspondence to V. V. Amel’kin.

Additional information

Original Russian Text © V.V. Amel’kin, M.N. Vasilevich, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 1, pp. 3–8.

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Amel’kin, V.V., Vasilevich, M.N. Construction of a Fuchs Equation with Four Given Finite Singular Points and Given Reducible 2 × 2 Monodromy Matrices. Diff Equat 54, 1–6 (2018). https://doi.org/10.1134/S0012266118010019

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  • DOI: https://doi.org/10.1134/S0012266118010019

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