Ukrainian Mathematical Journal

, Volume 36, Issue 2, pp 236–239 | Cite as

Connection between quadratic forms and the Green's function of a linear extension of dynamical systems on the torus

  • V. L. Kulik
Brief Communications


Dynamical System Quadratic Form Linear Extension 
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Literature cited

  1. 1.
    A. M. Samoilenko, “Preservation of invariant tori under perturbations,” Izv. Akad. Nauk SSSR, Ser. Mat.,34, 1219–1240 (1970).Google Scholar
  2. 2.
    I. U. Bronshtein, Extensions of Minimal Transformations Groups [in Russian], Shtiintsa, Kishinev (1975).Google Scholar
  3. 3.
    A. M. Samoilenko, “Green's function of a linear extension of a dynamical system on the torus, conditions for its uniqueness, and properties following from these conditions,” Ukr. Mat. Zh.,32, No. 6, 792–797 (1980).Google Scholar
  4. 4.
    A. M. Samoilenko and V. L. Kulik, “Continuity of the Green's function of the problem of an invariant torus,” Ukr. Mat. Zh.,30, No. 6, 779–788 (1978).Google Scholar
  5. 5.
    A. M. Samoilenko and V. L. Kulik, “Exponential dichotomy of an invariant torus of dynamical systems,” Differents. Uravn.,15, No. 8, 1434–1443 (1979).Google Scholar
  6. 6.
    Yu. A. Mitropol'skii and O. B. Lykova, Integral Manifolds in Nonlinear Mechanics [in Russian], Nauka, Moscow (1973).Google Scholar
  7. 7.
    N. N. Bogolyubov, Yu. A. Mitropol'skii, and A. M. Samoilenko, Method of Accelerated Convergence in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1969).Google Scholar
  8. 8.
    A. I. Perov and Yu. V. Trubnikov, “Monotone differential equations. IV,” Differents. Uravn.,14, No. 7, 1192–1202 (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • V. L. Kulik
    • 1
  1. 1.Institute of MathematicsAcademy of Sciences of the Ukrainian SSRKiev

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