Advertisement

Ukrainian Mathematical Journal

, Volume 27, Issue 2, pp 132–143 | Cite as

Invariant toroidal manifolds and resonances in discrete dynamical systems

  • A. S. Gurtovnik
  • V. P. Kogan
  • Yu. I. Neimark
Article
  • 17 Downloads

Keywords

Dynamical System Discrete Dynamical System Toroidal Manifold Invariant Toroidal Manifold 
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.

Literature cited

  1. 1.
    N. N. Bogolyubov and Yu. A. Mitropol'skii, “The method of integral manifolds in nonlinear mechanics,” Proceedings of the International Symposium on Nonlinear Oscillations, Vol. I [in Russian], Izdatel'stvo Akad. Nauk Ukrain. SSR, Kiev (1963).Google Scholar
  2. 2.
    N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Gosudarstvennoe Izdatel'stvo Fiziko-Matematicheskoi Literatury, Moscow (1963).Google Scholar
  3. 3.
    Yu. A. Mitropol'skii and O. B. Lykova, Lectures on the Method of Integral Manifolds [in Russian], Izdatel'stvo Instituta Matematiki Akad. Nauk Ukrain. SSR, Kiev (1968).Google Scholar
  4. 4.
    A. Khalanai and D. Veksler, Qualitative Theory of Impulsive Systems [Russian translation], Mir, Moscow (1971).Google Scholar
  5. 5.
    Yu. I. Neimark, The Method of Point Mappings in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1972).Google Scholar
  6. 6.
    D. I. Martynyuk, Lectures on the Qualitative Theory of Resonance Equations [in Russian], Naukova Dumka, Kiev (1972).Google Scholar
  7. 7.
    Yu. A. Mitropol'skii and A. M. Samoilenko, “On quasiperiodic oscillations in nonlinear systems,” Ukrain. Matem. Zh.,24. No. 2, 179–193 (1972).Google Scholar
  8. 8.
    E. P. Belan, “On the method of the mean in the theory of finite-difference equations,” Ukrain. Matem. Zh.19, No. 3 (1967).Google Scholar
  9. 9.
    J. Hale, Oscillations in Nonlinear Systems, McGraw Hill, New York (1963).Google Scholar
  10. 10.
    N. N. Moiseev, Asymptotic Methods of Nonlinear Mechanics [in Russian], Nauka, Moscow (1969).Google Scholar
  11. 11.
    V. M. Volosov and B. I. Morgunov, The Method of the Mean in the Theory of Nonlinear Oscillating Systems [in Russian], Izdatel'stvo Moskovokogo Gosudarstvennogo Universiteta, Moscow (1971).Google Scholar
  12. 12.
    B. M. Levitan, Almost Periodic Functions [in Russian], Gosudarstvennoe Izdatel'stvo Tekhnicheskoi Literatury, Moscow (1953).Google Scholar
  13. 13.
    L. A. Lyusternik and V. I. Sobolev, Elements of Functional Analysis [in Russian], Nauka, Moscow (1965).Google Scholar
  14. 14.
    Van-der Waerden, Modern Algebra [Russian translation], Ob'‘edinenie Gosudarstvennykh Izdatel’ stv, Moscow-Leningrad (1947).Google Scholar
  15. 15.
    V. I. Arnol'd, “Small elements and the problems of the stability of motion in the classical and the celestial mechanics, ”Ukrain. Matem. Zh.,18, No. 5 (1963).Google Scholar
  16. 16.
    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

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • A. S. Gurtovnik
    • 1
  • V. P. Kogan
    • 1
  • Yu. I. Neimark
    • 1
  1. 1.Applied Mathematics and Cybernetics Research InstituteGor'kii State UniversityUSSR

Personalised recommendations