Structure of the spectrum of the Schr\"odinger operator with almost-periodic potential in the vicinity of its left edge
Funkcionalʹnyj analiz i ego priloženiâ, Tome 19 (1985) no. 1, pp. 42-48.

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Ya. G. Sinai. Structure of the spectrum of the Schr\"odinger operator with almost-periodic potential in the vicinity of its left edge. Funkcionalʹnyj analiz i ego priloženiâ, Tome 19 (1985) no. 1, pp. 42-48. http://geodesic.mathdoc.fr/item/FAA_1985_19_1_a5/

[1] Dinaburg E.I., Sinai Ya.G., “Ob odnomernom uravnenii Shredingera s kvaziperiodicheskim potentsialom”, Funkts. analiz, 9:4 (1975), 8–21 | MR | Zbl

[2] Belokolos E.D., “Kvantovaya chastitsa v odnomernoi deformirovannoi reshetke. Otsenka razmerov lakun v spektre”, Teor. i mat. fizika, 25:3 (1975), 344–357 | MR

[3] Rüssman H., “On the one-dimensional Schrodinger equation with a quasi-periodic potential”, Ann. New York Acad. Sci., 357 (1980), 90–107 | DOI | MR | Zbl

[4] Bellisard J., Lima R., Testard D., “A metal-insulator transition for almost Mathieu model”, Comm. in Math. Physics, 88:2 (1983), 207–235 | DOI | MR

[5] Aubry S., “The twist map, the extended Frenkel–Kontorova model and the Devil's staircase”, Physica D, 7 (1983), 240–258 | DOI | MR

[6] Mozer Yu., Lektsii o gamiltonovykh sistemakh, Mir, M., 1973

[7] Lazutkin V.F., Terman D.Ya., “Percival's variational principle and commensurate-incommensurate phase transitions in one - dimensional chains”, Comm. in Math. Physics, 94:4 (1984), 511–522 | DOI | MR | Zbl

[8] Kozlov S.M., “Privodimost kvaziperiodicheskikh operatorov i usrednenie”, Trudy MMO, 46, 1983, 99–123 | MR

[9] Mozer Yu., “Bystro skhodyaschiisya iteratsionnyi metod i nelineinye uravneniya v chastnykh proizvodnykh”, UMN, 23:4 (1968), 179–238 | MR

[10] Mather J.N., “Existence of quasiperiodic orbits for twist homeomorphismus of the annulus”, Topology, 21 (1982), 457–467 | DOI | MR | Zbl

[11] Percival I.C., “Variational principle for invariant tori and cantori. Non-linear dynamics and the beam-beam interaction”, AIP Conf. Proc., no. 57, 1979, 302–310 | MR