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A contribution to the theory of Lyapunov exponents for linear systems of differential equations

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Literature cited

  1. B. F. Bylov, “Almost reducible systems,” Author's Abstract of Doctoral Dissertation, Physicomathematical Sciences, Minsk, Akad. Nauk BSSR (1966).

    Google Scholar 

  2. B. F. Bylov, “Reduction to block-triangular form, and necessary and sufficient conditions for the stability of characteristic exponents of a linea system of differential equations,” Differents. Uravn.,6, No. 2, 243–252 (1970).

    Google Scholar 

  3. B. F. Bylov, R. é. Vinograd, D. M. Grobman, and. V. V. Nemytskii, Theory of Lyapunov Exponents and Its Applications to Stability Problems [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  4. B. F. Bylov and N. A. Izobov, “Necessary and sufficient conditions for the stability of characteristic exponents of a linear system,” Differents. Ura.,5, No. 10, 1794–1803 (1969).

    Google Scholar 

  5. R. é. Vinograd, “On the central characteristic exponent of a system of differential equations,” Mat. Sb.,42, 207–222 (1957).

    Google Scholar 

  6. Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  7. B. P. Demidovich, Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  8. N. A. Izobov, “Linear systems of ordinary differential equations,” J. Sov. Math.,5, No. 1 (1976).

  9. N. A. Izobov, “The minimal exponent of a two-dimensional linear differential system,” Differents. Uravn.,13, No. 5, 848–858 (1977).

    Google Scholar 

  10. N. A. Izobov, “A lower bound for the minimal exponent of a linear system,” Differents. Uravn.,14, No. 9, 1576–1588 (1978).

    Google Scholar 

  11. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Graylock (1961).

  12. A. M. Lyapunov, General Problem of the Stability of Motion [in Russian], Gostekhizdat, Moscow-Leningrad (1950).

    Google Scholar 

  13. V. M. Millionshchikov, “A criterion for the smallness of the modification of the directions of solutions to a linear system of differential equations under small perturbations of the coefficients of the system,” Mat. Zametki4, No. 2, 173–180 (1968).

    Google Scholar 

  14. V. M. Millionshchikov, “Proof of the attainability of central exponents,” Sib. Mat. Zh.,10, No. 1, 99–104 (1969).

    Google Scholar 

  15. V. M. Millionshchikov, “On the instability of the special exponents and on the asymmetry of the almost reducibility relation of linear systems of differential equations.” Differents. Uravn.,5, No. 4, 749–750 (1969).

    Google Scholar 

  16. V. M. Millionshchikov, “Systems with integral separateness are dense in the set of all linear systems of differential equations,” Differents. Uravn.,5, No. 7, 1167–1170 (1969).

    Google Scholar 

  17. V. M. Millionshchikov, “Structurally stable properties of linear systems of differential equations,” Differents. Uravn.,5, No. 10, 1775–1784 (1969).

    Google Scholar 

  18. K. P. Persidskii, “On the stability of motion in the first approximation,” Mat. Sb.,40, No. 3, 284–292 (1933).

    Google Scholar 

  19. I. G. Petrovskii, Lectures on the Theory of Ordinary Differential Equations [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  20. M. M. Postnikov, Lectures on Geometry. IInd Semester. Linear Algebra and Differential Geometry [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  21. I. N. Sergeev, “Exact upper bounds of mobility for the Lyapunov exponents of a system of differential equations and the behavior of exponents under perturbations that tend to zero at infinity,” Differents. Uravn.,16, No. 3, 438–448 (1980).

    Google Scholar 

  22. I. N. Sergeev, “On the open nucleus of the set of systems of differential equations with one stable Lyapunov exponent,” Differents. Uravn.,16, No. 6, 1135–1137 (1980).

    Google Scholar 

  23. I. N. Sergeev, “Invariance of central exponents under perturbations that tend to zero at infinity,” Differents. Uravn.,16, No. 9, 1719 (1980).

    Google Scholar 

  24. I. N. Sergeev, “Some problems in the theory of stability of Lyapunov exponents, Annotation of a report in the paper: On the seminar on the qualitative theory of differential equations held at the Moscow University,” Differents. Uravn.,16, No. 10, 1903–1904 (1980).

    Google Scholar 

  25. O. Perron, “Die Ordnungszahlen der Differentialgleichungen,” Math. Z.,32, 703–728 (1930).

    Google Scholar 

  26. O. Perron, “üblineare Differentialgleichungen, bei denen die unabhangige Variable reel ist,” J. Reine Angew. Math.,142, 254–270 (1931).

    Google Scholar 

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Authors
  1. N. N. Sergeev
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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 9, pp. 111–166, 1983.

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Sergeev, N.N. A contribution to the theory of Lyapunov exponents for linear systems of differential equations. J Math Sci 33, 1245–1292 (1986). https://doi.org/10.1007/BF01084752

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  • DOI: https://doi.org/10.1007/BF01084752

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