Exponential estimates on the one-dimensional Schroedinger equation with bounded analytic potential
Annales de l'I.H.P. Physique théorique, Volume 51 (1989) no. 1, p. 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},
     publisher = {Gauthier-Villars},
     volume = {51},
     number = {1},
     year = {1989},
     pages = {45-66},
     zbl = {0713.34054},
     mrnumber = {1029849},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1989__51_1_45_0}
}
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, Volume 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 197830 | Zbl 0158.09604

[2] E. Trubowitz, Commun. Pure Appl. Math., Vol. 30, 1977, pp. 321-337. | MR 430403 | Zbl 0403.34022

[3] A. Voros, Ann. Inst. Henri-Poincaré, Vol. 29, 1983, pp. 211-338. | Numdam | MR 729194 | Zbl 0526.34046

[4] A. Grigis, Ann. Scient. Ec. Norm. Sup., 4e serie, Vol. 20, 1987, pp. 641-672. | Numdam | MR 932802 | Zbl 0644.34021

[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 801035

[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 880535 | Zbl 0662.70022

[8] A.I. Neishtadt, Prikl. Matem. Mekan., Vol. 45, 1981, p. 80 (PMM U.S.S.R., Vol. 45, 1982, p. 58). | MR 654778 | Zbl 0488.70016

[9] A. Giorgilli and L. Galgani, Celestial Mechanics, Vol. 37, 1985, p. 95. | MR 838181

[10] G. Benettin and G. Gallavotti, J. Stat. Phys., Vol. 44, 1985, p. 293. | MR 857061 | Zbl 0636.70018

[11] F. Delyon and P. Foulon: J. Stat. Phys., Vol. 45, 1986, pp. 41-47; Vol. 49, 1987, pp. 829-840. | Zbl 0628.34052

[12] G. Benettin, L. Galgani and A. Giorgilli, Comm. Math. Phys., Vol. 113, 1987, p. 87. | MR 918407 | Zbl 0646.70013

[13] G. Benettin, L. Galgani and A. Giorgilli, Comm. Math. Phys., Vol. 121, 1989, p. 557. | MR 990993 | Zbl 0679.70015

[14] M.V. Fedoryuk, Differentsial'nye Uravneniya, Vol. 12, 1976, pp. 1012-1018 (Diff. Eq., Vol. 12, 1976, pp. 713-718). | MR 428941

[15] E.I. Dinaburg and Ya. G. Sinai, Functional Anal. Appl., Vol. 9, 1975, pp. 279-289. | Zbl 0333.34014

[16] H. Rüssmann, Ann. N. Y. Acad. Sci., Vol. 357, 1980, pp. 90-107. | MR 612810 | Zbl 0477.34007

[17] J. Moser and J. Pöschel, Comment. Math. Helvetici, Vol. 59, 1984, pp. 39-85. | MR 743943 | Zbl 0533.34023

[18] L. Chierchia, J. Math. Phys., Vol. 28, 1987, pp. 2891-2898. | Zbl 0642.34018

[19] M. Reed and B. Simon, Methods of modern mathematical phisics, Vol. 3: Scattering theory, Academic Press, New York, 1979. | MR 529429 | Zbl 0405.47007

[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 467824 | Zbl 0319.35017

[21] H. Rüssmann, Comm. Pure Appl. Math., Vol. 29, 1976, p. 755. | MR 426054

[22] B. Simon, J. Funct. Anal., Vol. 42, 1981, pp. 347-355. | MR 626449 | Zbl 0471.47028

[23] J. Avron and B. Simon, Ann. Phys. (N.Y.), Vol. 134, 1980, pp. 76-84. | MR 626698 | Zbl 0464.34020

[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 0722.34070