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Integral symmetries, integral invariants, and monodromy matrices for ordinary differential equations

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Abstract

We consider the transfer and monodromy matrices for the degenerate Heun equation. We use an auxiliary ordinary third-order linear differential equation that is “stable” under the integral Euler transformation. We find the invariant of this transformation and express it via the transfer matrix element.

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References

  1. A. Erdély et al., eds.,Higher Transcendental Functions (Based on notes left by H. Bateman), Vol. 1, McGraw-Hill, New York (1953).

    Google Scholar 

  2. I. S. Gradshtein and I. M. Ryzhik,Tables of Integrals, Series, and Products [in Russian], Gos. Izd. Fiz.-Mat. Lit., Moscow (1962); English transl., Acad. Press, New York (1969).

    Google Scholar 

  3. M. Abramovitz and I. A. Stegun,Handbook of Mathematical Functions, Dover, New York (1968).

    Google Scholar 

  4. A. Seeger and W. Lay, eds.,Centennial Workshop on Heun's Equation, Max-Plank-Institut für Metalforshung, Stuttgart (1990).

    Google Scholar 

  5. A. Erdelyi,Quart. J. Math.,13, 107 (1942).

    Article  MathSciNet  Google Scholar 

  6. D. I. Abramov and I. V. Komarov,Theor. Math. Phys.,29, 1041 (1976).

    Article  MathSciNet  Google Scholar 

  7. B. C. Carlson,SIAM J. Math. Anal.,11, 325 (1980).

    Article  Google Scholar 

  8. G. Valen,SIAM J. Math. Anal.,17, 688 (1986).

    Article  MathSciNet  Google Scholar 

  9. A. Ya. Kazakov,Diff. Uravn.,22, 354 (1986).

    MathSciNet  Google Scholar 

  10. A. Ya. Kazakov and S. Yu. Slavyanov,Meth. Appl. Anal.,3, 447 (1996).

    MathSciNet  Google Scholar 

  11. A. Ya. Kazakov and S. Yu. Slavyanov,Theor. Math. Phys.,107, 733 (1996).

    Article  MathSciNet  Google Scholar 

  12. W. Buhring, “A linear differential equation with two irregular singular points of rank one,” inCentennial Workshop on Heun's Equation (A. Seeger and W. Lay, eds.), Max-Plank Institute fur Metalforshung, Stuttgart (1990), p. 38.

    Google Scholar 

  13. A. A. Bolibrukh,The 21st Hilbert Problem for Linear Fuchsian Systems [in Russian], (Proceedings of the Steklov Mathematical Institute, Vol. 206), Nauka, Moscow (1994); English transl., Amer. Math. Soc., Providence, RI (1995).

    MATH  Google Scholar 

  14. E. Hille,Ordinary Differential Equations in the Complex Domain, Dover, New York (1997).

    MATH  Google Scholar 

  15. I. V. Komarov, L. I. Ponomarev, and S. Yu. Slavyanov,Spheroidal and Spheroidal Coulomb Functions [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  16. F. G. Tricomi,Differential Equations, Blackie, London (1961).

    MATH  Google Scholar 

  17. V. V. Golubev,Lectures on the Analytic Theory of Differential Equations [in Russian], Gostekhizdat, Moscow (1941).

    Google Scholar 

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Authors and Affiliations

  1. St. Petersburg State University of Aerospace Instrumentation, Russia

    A. Ya. Kazakov

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  1. A. Ya. Kazakov
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Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 116, No. 3, pp. 323–335, September, 1998.

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Kazakov, A.Y. Integral symmetries, integral invariants, and monodromy matrices for ordinary differential equations. Theor Math Phys 116, 991–1000 (1998). https://doi.org/10.1007/BF02557140

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  • DOI: https://doi.org/10.1007/BF02557140

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