Ukrainian Mathematical Journal

, Volume 54, Issue 3, pp 504–510 | Cite as

On Some Properties of the Behavior of Linear Extensions of Dynamical Systems on a Torus under Perturbation of Phase Variables

  • A. M. Samoilenko
  • N. V. Stepanenko


We investigate classes of linear extensions of dynamical systems on a torus for which the Lyapunov functions exist for an arbitrary flow on the torus. Linear extensions for which the Lyapunov functions exist only with varying coefficients are considered separately. We investigate the problem of preservation of regularity under perturbation of phase variables.


Dynamical System Lyapunov Function Phase Variable Linear Extension Arbitrary Flow 


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  1. 1.
    Yu. A. Mitropol'skii, A. M. Samoilenko, and V. L. Kulik, Investigation of Dichotomy of Linear Systems of Differential Equations Using Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1990).Google Scholar
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    A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Nauka, Moscow (1987); English translation: Kluwer, Dordrecht (1991).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • A. M. Samoilenko
    • 1
  • N. V. Stepanenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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