Ukrainian Mathematical Journal

, Volume 56, Issue 8, pp 1276–1299 | Cite as

Reducibility of a nonlinear oscillation system with pulse influence in the neighborhood of an integral manifold

  • A. M. Samoilenko
  • R. I. Petryshyn
  • P. M. Dudnyts’kyi


In the neighborhood of an asymptotically stable integral manifold of a multifrequency system with pulse influence at fixed times, we perform a decomposition of the equations for angular and position variables.


Fixed Time Nonlinear Oscillation Position Variable Oscillation System Integral Manifold 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. M. Samoilenko, Investigation of a Dynamical System in the Neighborhood of a Quasiperiodic Trajectory [in Russian], Preprint 90.35, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1990).Google Scholar
  2. 2.
    A. M. Samoilenko, “Investigation of a dynamical system in the neighborhood of an invariant toroidal manifold,” Ukr. Mat. Zh., 42, No.4, 530–537 (1991).Google Scholar
  3. 3.
    A. M. Samoilenko and M. Ya. Svishchuk, “On the decomposition of a system of differential equations with slowly varying phase in the neighborhood of an asymptotically stable invariant torus,” Ukr. Mat. Zh., 37, No.6, 751–756 (1985).Google Scholar
  4. 4.
    A. M. Samoilenko and R. I. Petryshyn, Multifrequency Oscillations of Nonlinear Systems [in Ukrainian], Institute of Mathe-matics, Ukrainian Academy of Sciences, Kyiv (1998).Google Scholar
  5. 5.
    V. V. Strygin and V. A. Sobolev, Separation of Motions by the Method of Integral Manifolds [in Russian], Nauka, Moscow (1988).Google Scholar
  6. 6.
    A. M. Samoilenko, R. I. Petryshyn, and T. M. Sopronyuk, “Construction of an integral manifold of a multifrequency oscillation system with fixed times of pulse influence,” Ukr. Mat. Zh., 55, No.5, 641–662 (2003).Google Scholar
  7. 7.
    A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • A. M. Samoilenko
    • 1
  • R. I. Petryshyn
    • 2
  • P. M. Dudnyts’kyi
    • 2
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKyiv
  2. 2.Chernivtsi UniversityChernivtsi

Personalised recommendations