Geodesic
Perturbation of quasiperiodic solutions of infinite-dimensional Hamiltonian systems
Izvestiya. Mathematics, Tome 32 (1989) no. 1, pp. 39-62 
S. B. Kuksin. Perturbation of quasiperiodic solutions of infinite-dimensional Hamiltonian systems. Izvestiya. Mathematics, Tome 32 (1989) no. 1, pp. 39-62. http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a2/
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     title = {Perturbation of quasiperiodic solutions of infinite-dimensional {Hamiltonian} systems},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A theorem on preservation of quasiperiodic solutions under small perturbations of the Hamiltonian is proved for a certain class of infinite-dimensional Hamiltonian systems. Hamiltonian perturbations of the one-dimensional Schrödinger equation are considered as examples. Bibliography: 10 titles.

[1] Arnold V. I., “Dokazatelstvo teoremy A. N. Kolmogorova o sokhranenii uslovno-periodicheskikh dvizhenii pri malom izmenenii funktsii Gamiltona”, UMN, 18:1 (1963), 13–39

[2] Mozer Yu., “Bystro skhodyaschiisya metod iteratsii i nelineinye differentsialnye uravneniya”, UMN, 23:4 (1968), 179–238 | MR

[3] Melnikov V. K., “Ob odnom semeistve uslovno-periodicheskikh reshenii sistemy Gamiltona”, Dokl. AN SSSR, 181:3 (1968), 546–549 | MR

[4] Mozer Yu., “O razlozhenii uslovno-periodicheskikh dvizhenii v skhodyaschiesya stepennye ryady”, UMN, 24:2 (1969), 165–211 | MR

[5] Nikolenko N. V., “Metod normalnykh form Puankare v zadachakh integriruemosti uravnenii evolyutsionnogo tipa”, UMN, 41:5 (1986), 109–152 | MR | Zbl

[6] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR

[7] Krasnoselskii M. A., Zabreiko P. D., Pustylnik E. I., Sobolevskii P. E., Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966 | MR

[8] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl

[9] Lankaster P., Teoriya matrits, 2-e izd., Nauka, M., 1982 | MR

[10] Chernoff P. R., Marsden J. E., Properties of infinite dimensional Hamiltonian systems, Lecture Notes in Mathematics, 425, Berlin, 1974 | MR | Zbl