Advertisement

Ukrainian Mathematical Journal

, Volume 54, Issue 4, pp 613–628 | Cite as

On Invariant Tori of Itô Stochastic Systems

  • A. M. Samoilenko
  • A. N. Stanzhitskii
Article
  • 19 Downloads

Abstract

By using the Green–Samoilenko function, we establish conditions for the existence of invariant sets of Itô stochastic systems that are extensions of dynamical systems on a torus.

Keywords

Dynamical System Stochastic System Samoilenko Function 
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.
    O. M. Stanzhyts'kyi, “Investigation of stability of invariant sets using local coordinates,” Nelin. Kolyvannya, 3, No. 2, 266–270 (2000).Google Scholar
  2. 2.
    I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1982).Google Scholar
  3. 3.
    A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Nauka, Moscow (1987).Google Scholar
  4. 4.
    E. F. Tsar'kov, Random Perturbations of Functional Differential Equations [in Russian], Zinatne, Riga (1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • A. M. Samoilenko
    • 1
  • A. N. Stanzhitskii
    • 2
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev
  2. 2.Shevchenko Kiev National UniversityKiev

Personalised recommendations