Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Decomposability of linearized systems of differential equations

  • 20 Accesses

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    Ju. L. Daleckii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space, Am. Math. Soc. (1974).

  2. 2.

    E. N. Rozenvasser, Lyapunov Exponents in the Theory of Linear Systems of Control [in Russian], Nauka, Moscow (1977).

  3. 3.

    B. F. Bylov, É. R. Vinograd, V. Ya. Lin, and O. V. Lokutsievskii, “Topological causes of anomalous behavior of certain almost periodic systems,” in: Problems of the Asymptotic Theory of Nonlinear Oscillations [in Russian], Naukova Dumka, Kiev (1977), pp. 54–61.

  4. 4.

    V. M. Millionshchikov, “Structure of fundamental matrices with almost periodic coefficients,” Dokl. Akad. Nauk SSSR,171, No. 2, 288–291 (1966).

  5. 5.

    B. F. Bylov, “Structure of solutions of systems of linear differential equations,” Mat. Sb.,66, No. 2, 215–229 (1965).

  6. 6.

    N. N. Bogolyubov, Yu. A. Mitropol'skii, and A. M. Samoilenko, The Method of Accelerated Convergence in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1969).

  7. 7.

    Yu. A. Mitropol'skii and A. M. Samoilenko, “Quasiperiodic oscillations in nonlinear systems,” Ukr. Mat. Zh., 24, No. 2, 179–193 (1972).

  8. 8.

    Yu. A. Mitropol'skii and O. B. Lykova, Integral Manifolds in Nonlinear Mechanics [in Russian], Nauka, Moscow (1973).

  9. 9.

    A. M. Samoilenko, “Quasiperiodic solutions of a system of linear algebraic equations with periodic coefficients,” in: Analytic Methods of Investigation of Solutions of Nonlinear Differential Equations [in Russian], Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1975), pp. 5–26.

  10. 10.

    A. M. Samoilenko and V. L. Kulik, “Existence of a Green's function for the problem of an invariant torus,” Ukr. Mat. Zh.,27, No. 3, 348–359 (1975).

Download references

Author information

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 34, No. 5, pp. 587–593, September–October, 1982.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Samoilenko, A.M., Kulik, V.L. Decomposability of linearized systems of differential equations. Ukr Math J 34, 475–480 (1982). https://doi.org/10.1007/BF01093134

Download citation

Keywords

  • Differential Equation