Differential Equations

, Volume 36, Issue 1, pp 120–131 | Cite as

Moduli of continuity of the derivatives of invariant tori for linear extensions of dynamical systems

  • A. M. Samoilenko
  • A. A. Burilko
  • I. N. Grod
Ordinary Differential Equations

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bogolyubov, N.N., Mitropol’skii, Yu.A., and Samoilenko, A.M.,Metod uskorennoi skhodimosti v nelineinoi mekhanike (The Method of Accelerated Convergence in Nonlinear Mechanics), Kiev, 1969.Google Scholar
  2. 2.
    Hale, J.,Oscillations in Nonlinear Systems, McGraw-Hill, New York-Toronto-London, 1963. Translated under the titleKolebaniya v nelineinykh sistemakh, Moscow, 1996.MATHGoogle Scholar
  3. 3.
    Kurzweil, J.,Differents. Uravn., 1968, vol. 4, no. 5, pp. 785–797.MathSciNetGoogle Scholar
  4. 4.
    Moser, J.,Nachr. Acad. Wiss. Göttingen Math.-Phis. Kl., 1962, vol. 18a, no. 1, pp. 1–20.Google Scholar
  5. 5.
    Sacker, R.J.,J. Math., and Mech., 1969, vol. 18, no. 8, pp. 705–761.MATHMathSciNetGoogle Scholar
  6. 6.
    Samoilenko, A.S.,Izv. Akad. Nauk SSSR. Ser. Mat., 1970, vol. 34, no. 6, pp. 1219–1240.MathSciNetGoogle Scholar
  7. 7.
    Mitropol’skii, Yu.A., Samoilenko, A.M., and Kulik, V.L.,Issledovanie dikhotomii sistem lineinykh differentsial’nykh uravnenii s pomoshch’yu funktsii Lyapunova (Investigation of Dichotomy of Systems of Linear Differential Equations with the Use of Lyapunov Function), Kiev, 1990.Google Scholar
  8. 8.
    Bronshtein, I.U. and Kopanskii, A.Ya.,Invariantnye mnogoobraziya i normal’nye formy (Invariant Manifolds and Normal Forms), Kishinev, 1992.Google Scholar
  9. 9.
    Grad, I.N. and Kulik, V.L.,Ukr. Mat. Zh., 1989, vol. 41, no. 12, pp. 1709–1714.Google Scholar
  10. 10.
    Samoilenko, A.M. and Kulik, V.L.,Differents. Uravn., 1997, vol. 30, no. 6, pp. 779–788.MathSciNetGoogle Scholar
  11. 11.
    Samoilenko, A.M. and Burilko, A.A.,Ukr. Mat. Zh., 1998, vol. 51, no. 4, pp. 570–584.MathSciNetGoogle Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2000

Authors and Affiliations

  • A. M. Samoilenko
    • 1
    • 2
  • A. A. Burilko
    • 1
    • 2
  • I. N. Grod
    • 1
    • 2
  1. 1.Institute for MathematicsNational Academy of SciencesUkraine
  2. 2.Ternopol State Pedagogical UniversityUkraine

Personalised recommendations