Advertisement

Ukrainian Mathematical Journal

, Volume 45, Issue 12, pp 1869–1877 | Cite as

Reducibility of linear systems of difference equations with almost periodic coefficients

  • Yu. A. Mitropol'skii
  • D. I. Martynyuk
  • V. I. Tynnyi
Article
  • 38 Downloads

Abstract

We establish sufficient conditions of the reducibility of the linear system of difference equationsx(t+1)=Ax(t) + P(t) x(t) with an almost periodic matrixP(t) to a system with a constant matrix.

Keywords

Linear System Difference Equation Constant Matrix Periodic Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. I. Martynyuk and N. A. Perestyuk, “On reducibility of linear systems of difference equations with quasiperiodic coefficients,”Vychisl. Prikl. Mat., issue 23, 116–127 (1974).Google Scholar
  2. 2.
    D. I. Martynyuk and N. A. Perestyuk, “Reducibility of linear systems of difference equations with smooth right-hand side,”Vychisl. Prikl. Mat., Issue 27, 34–40 (1976).Google Scholar
  3. 3.
    Yu. A. Mitropol'skii, A. M. Samoilenko, and D. I. Martynyuk,Systems of Evolution Equations with Periodic and Conditionally Periodic Coefficients [in Russian], Naukova Dumka, Kiev (1984).Google Scholar
  4. 4.
    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).Google Scholar
  5. 5.
    Yu. A. Mitropol'skii and A. M. Samoilenko, “Construction of solutions of linear differential equations with quasiperiodic coefficients,” in:Mathematical Physics [in Russian], Naukova Dumka, Kiev (1967), pp. 185–198.Google Scholar
  6. 6.
    Yu. A. Mitropol'skii and A. M. Samoilenko, “Construction of solutions of linear differential equations with quasiperiodic coefficients by the method of accelerated convergence,”Ukr. Mat. Zh.,17, No. 6, 42–59 (1965).Google Scholar
  7. 7.
    A. M. Samoilenko, “Reducibility of systems of linear differential equations with quasiperiodic coefficients,”Ukr. Mat. Zh.,20, No. 2, 279–281 (1968).Google Scholar
  8. 8.
    M. G. Filippov, “Reducibility of systems of linear differential equations with almost periodic coefficients,” in:Asymptotic Methods and Applications to Problems of Mathematical Physics [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1990), pp. 132–137.Google Scholar
  9. 9.
    A. G. Baskakov, “The theorem on reducibility of linear differential equations with quasiperiodic coefficients,”Ukr. Mat. Zh.,35, No. 4, 416–421 (1983).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Yu. A. Mitropol'skii
    • 1
  • D. I. Martynyuk
    • 2
  • V. I. Tynnyi
    • 2
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev
  2. 2.Kiev UniversityKiev

Personalised recommendations