Literature Cited
V. E. Zakharov, “Hamiltonian formalism for waves in nonlinear media with dispersion”, Radiofizika,17, No. 4, 431–453 (1974).
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).
V. I. Arnol'd, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York (1978).
V. K. Mel'nikov, “A family of quasiperiodic solutions of a Hamilton system”, Dokl. Akad. Nauk SSSR,181, No. 3, 546–549 (1968).
J. Moser, “Convergent series expansions for quasiperiodic motions”, Math. Ann.,169, 136–176 (1967).
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).
N. V. Nikolenko, “Invariant asymptotically stable tori of the perturbed Korteweg-de-Vries equation”, Usp. Mat. Nauk,35, No. 5, 121–180 (1980).
H. Brezis, Operateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam (1973).
J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Springer-Verlag, New York (1972).
P. Halmos and V. Sunder, Bounded Integral Operators on L2-Spaces, Springer-Verlag, New York (1978).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Academic Press, New York (1972–1977).
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).
S. M. Graff, “On the conservation of hyperbolic invariant tori for Hamiltonian systems”, J. Diff. Equations,15, No. 1, 1–69 (1974).
P. R. Chernoff and J. E. Marsden, “Properties of infinite dimensional Hamiltonian systems”, Lect. Notes Math., No. 425, Springer-Verlag, Berlin (1974).
Additional information
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.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02577134