Exponential estimates on the one-dimensional Schroedinger equation with bounded analytic potential
Annales de l'I.H.P. Physique théorique, Tome 51 (1989) no. 1, pp. 45-66.
@article{AIHPA_1989__51_1_45_0,
     author = {Benettin, Giancarlo and Chierchia, Luigi and Fass\`o, Francesco},
     title = {Exponential estimates on the one-dimensional {Schroedinger} equation with bounded analytic potential},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {45--66},
     publisher = {Gauthier-Villars},
     volume = {51},
     number = {1},
     year = {1989},
     mrnumber = {1029849},
     zbl = {0713.34054},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1989__51_1_45_0/}
}
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Benettin, Giancarlo; Chierchia, Luigi; Fassò, Francesco. Exponential estimates on the one-dimensional Schroedinger equation with bounded analytic potential. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) no. 1, pp. 45-66. http://www.numdam.org/item/AIHPA_1989__51_1_45_0/

[1] W. Magnus and S. Winkler, Hill's Equation, Wiley and Sons, New York, 1966. | MR | Zbl

[2] E. Trubowitz, Commun. Pure Appl. Math., Vol. 30, 1977, pp. 321-337. | MR | Zbl

[3] A. Voros, Ann. Inst. Henri-Poincaré, Vol. 29, 1983, pp. 211-338. | Numdam | MR | Zbl

[4] A. Grigis, Ann. Scient. Ec. Norm. Sup., 4e serie, Vol. 20, 1987, pp. 641-672. | Numdam | MR | Zbl

[5] N.N. Nekhorosev, Usp. Mat. Nauk, Vol. 32, 1977 [Russ. Math. Surv., Vol. 32, 1, 1977].

[6] N.N. Nekhoroshev, Trudy Sem. Petrows., No. 5, 1979, p. 5 [Topics in Modern Mathematics, Petrovskii Sem. No. 5, O.A. Oleinik editor (Consultant Bureau, New York, 1985)]. | MR

[7] G. Gallavotti, Quasi-Integrable Mechanical Systems, in Critical phenomena, Random Systems, Gauge Theories, K. OSTERWALDER and R. STORA Eds., Les Houches, Session XLIII, 1984 (North-Holland, Amsterdam, 1986). | MR | Zbl

[8] A.I. Neishtadt, Prikl. Matem. Mekan., Vol. 45, 1981, p. 80 (PMM U.S.S.R., Vol. 45, 1982, p. 58). | MR | Zbl

[9] A. Giorgilli and L. Galgani, Celestial Mechanics, Vol. 37, 1985, p. 95. | MR

[10] G. Benettin and G. Gallavotti, J. Stat. Phys., Vol. 44, 1985, p. 293. | MR | Zbl

[11] F. Delyon and P. Foulon: J. Stat. Phys., Vol. 45, 1986, pp. 41-47; Vol. 49, 1987, pp. 829-840. | Zbl

[12] G. Benettin, L. Galgani and A. Giorgilli, Comm. Math. Phys., Vol. 113, 1987, p. 87. | MR | Zbl

[13] G. Benettin, L. Galgani and A. Giorgilli, Comm. Math. Phys., Vol. 121, 1989, p. 557. | MR | Zbl

[14] M.V. Fedoryuk, Differentsial'nye Uravneniya, Vol. 12, 1976, pp. 1012-1018 (Diff. Eq., Vol. 12, 1976, pp. 713-718). | MR

[15] E.I. Dinaburg and Ya. G. Sinai, Functional Anal. Appl., Vol. 9, 1975, pp. 279-289. | Zbl

[16] H. Rüssmann, Ann. N. Y. Acad. Sci., Vol. 357, 1980, pp. 90-107. | MR | Zbl

[17] J. Moser and J. Pöschel, Comment. Math. Helvetici, Vol. 59, 1984, pp. 39-85. | MR | Zbl

[18] L. Chierchia, J. Math. Phys., Vol. 28, 1987, pp. 2891-2898. | Zbl

[19] M. Reed and B. Simon, Methods of modern mathematical phisics, Vol. 3: Scattering theory, Academic Press, New York, 1979. | MR | Zbl

[20] H. Rüssmann, On Optimal Estimates for the Solutions of Linear Partial Differential Equations of first Order with Constant Coefficients on the Torus, in Dynamical Systems, Theory and Applications, J. MOSER Ed., Lect. Notes Phys., No. 38, Springer-Verlag, Berlin, 1975. | MR | Zbl

[21] H. Rüssmann, Comm. Pure Appl. Math., Vol. 29, 1976, p. 755. | MR

[22] B. Simon, J. Funct. Anal., Vol. 42, 1981, pp. 347-355. | MR | Zbl

[23] J. Avron and B. Simon, Ann. Phys. (N.Y.), Vol. 134, 1980, pp. 76-84. | MR | Zbl

[24] J. Fröhlich, T. Spencer and P. Wittwer, Localization for a class of one-dimensional quasi-periodic Schroedinger operators, to appear in Comm. Math. Phys. | Zbl