Ukrainian Mathematical Journal

, Volume 44, Issue 12, pp 1560–1568 | Cite as

Study of a discrete dynamic system in a neighborhood of a quasi-periodic trajectory

  • A. M. Samoilenko
Article

Abstract

We study a discrete system in a neighborhood of a quasi-periodic trajectory. We obtain conditions for reducing a system in this neighborhood to a system with quasi-periodic coefficients. We determine the behavior of this system under the action of small perturbations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. M. Samoilenko, “Investigation of dynamic systems in a neighborhood of a quasi-periodic trajectory,” Preprint 90.35, Akad. Nauk Ukr. SSR, Inst. Mat. (1990).Google Scholar
  2. 2.
    A. M. Samoilenko, “Dynamic systems in δm × En,” Ukr. Mat. Zh.,43, No. 10, 1283–1298 (1991).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.
    A. Halanay and D. Wexler, The Qualitative Theory of Systems with Impulse [Russian translation], Mir, Moscow (1971).Google Scholar
  5. 5.
    Yu. I. Neimark, The Method of Point Transformations in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1972).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • A. M. Samoilenko
    • 1
  1. 1.Mathematics InstituteAcademy of Sciences of the UkraineKiev

Personalised recommendations