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Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum

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Literature Cited

  1. V. E. Zakharov, “Hamiltonian formalism for waves in nonlinear media with dispersion”, Radiofizika,17, No. 4, 431–453 (1974).

    Google Scholar 

  2. V. I. Arnol'd, “Proof of a theorem of A. N. Kolmogorov on the conservation of quasiperiodic motions under a small change of the Hamilton function”, Usp. Mat. Nauk,18, No. 1, 13–39 (1963).

    Google Scholar 

  3. V. I. Arnol'd, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York (1978).

    Google Scholar 

  4. V. K. Mel'nikov, “A family of quasiperiodic solutions of a Hamilton system”, Dokl. Akad. Nauk SSSR,181, No. 3, 546–549 (1968).

    MathSciNet  Google Scholar 

  5. J. Moser, “Convergent series expansions for quasiperiodic motions”, Math. Ann.,169, 136–176 (1967).

    Article  MATH  MathSciNet  Google Scholar 

  6. N. V. Nikolenko, “Poincare's method of normal forms in the problems of intergrability of evolution-type equations”, Usp. Mat. Nauk,41, No. 5, 109–152 (1986).

    MathSciNet  Google Scholar 

  7. N. V. Nikolenko, “Invariant asymptotically stable tori of the perturbed Korteweg-de-Vries equation”, Usp. Mat. Nauk,35, No. 5, 121–180 (1980).

    MATH  MathSciNet  Google Scholar 

  8. H. Brezis, Operateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam (1973).

    Google Scholar 

  9. J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Springer-Verlag, New York (1972).

    Google Scholar 

  10. P. Halmos and V. Sunder, Bounded Integral Operators on L2-Spaces, Springer-Verlag, New York (1978).

    Google Scholar 

  11. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Academic Press, New York (1972–1977).

    Google Scholar 

  12. V. K. Mel'nikov, “Some cases of conservation of quasiperiodic motions under a small change of the Hamilton function”, Dokl. Akad. Nauk SSSR,165, No. 6, 1245–1248 (1965).

    MathSciNet  Google Scholar 

  13. S. M. Graff, “On the conservation of hyperbolic invariant tori for Hamiltonian systems”, J. Diff. Equations,15, No. 1, 1–69 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  14. P. R. Chernoff and J. E. Marsden, “Properties of infinite dimensional Hamiltonian systems”, Lect. Notes Math., No. 425, Springer-Verlag, Berlin (1974).

    MATH  Google Scholar 

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Institute of Control Problems, Academy of Sciences of the USSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 21, No. 3, pp. 22–37, July–September, 1987.

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Kuksin, S.B. Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum. Funct Anal Its Appl 21, 192–205 (1987). https://doi.org/10.1007/BF02577134

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