The quantum stability problem for time-periodic perturbations of the harmonic oscillator

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1. [1] E. Abrahams, P.W. Anderson, D.C. Licciardello and T.V. Ramakrishnan, Phys. Rev. Letters, t. 42, 1979, p. 673-676. 
2. [2] W. Amrein, V. Georgescu, Helv. Phys. Acta, t. 47, 1974, p. 517-533. MR366278
3. [3] V. Arnol'd, Russian Math. Surveys, t. 18, n° 5, 1963, p. 9-36. Zbl0129.16606
4. [4] J. Avron, B. Simon, Bull. A. M. S., t. 6, 1982, p. 81-86. Zbl0491.47014MR634437
5. [5] J. Bellissard, Trends and Developments in the Eighties, S. Albeverio and Ph. Blanchard, eds. World Sci. Pub., Singapour, 1985. MR853742
6. [6] J. Bellissard, R. Lima, E. Scoppola, Commun. Math. Phys., t. 88, 1983, p. 465-477. Zbl0543.35018MR702564
7. [7] J. Bellissard, R. Lima, D. Testard, Commun. Math. Phys., t. 88, 1983, p. 207-234. Zbl0542.35059MR696805
8. [8] G. Casati, I. Guarneri, Commun. Math. Phys., t. 95, 1984, p. 121-127. Zbl0581.46062MR757057
9. [9] M. Combescure, Ann. Inst. Henri Poincaré, t. 44, 1986, p. 293-314. Zbl0613.46064MR846470
10. [10] M. Combescure, Ann. of Physics, t. 173, 1987, p. 210-225. MR870892
11. [11] M. Combescure (in preparation). 
12. [12] W. Craig, Commun. Math. Phys., t. 88, 1983, p. 113-131. Zbl0525.35076MR691202
13. [13] A. Ya. GORDON, Usp. Mat. Nauk, t. 31, 1976, p. 257. Zbl0342.34012
14. [14] M. Hermann, Publ. IHES, t. 49. 
15. [15] J.S. Howland, Caltech, 1986. 
16. [16] A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, t. 98, 1954, p. 527-530. Zbl0056.31502MR68687
17. [17] J. Moser, Nachr. Akad. Wiss. Gott. Math. Phys. K, t. 1, 1962, p. 1-20. Zbl0107.29301MR147741
18. [18] J. Moser, Stable and Random Motions in Dynamical Systems. Princeton University Press, 1973. Zbl0271.70009MR442980
19. [19] J. Nash, Ann. of Math., t. 63, 1956, p. 20-63. Zbl0070.38603MR75639
20. [20] W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, Phys. Rev. A, t. 122, 1980, p. 1137-1140. 
21. [21] J. Pöschel, Commun. Math. Phys., t. 88, 1983, p. 447-464. Zbl0532.35070MR702563
22. [22] J. Pöschel, Commun. Pure and Applied Math., t. 35, 1982, p. 653-696. Zbl0542.58015
23. [23] D. Ruelle, Nuovo Cimento A, t. 61, 1969, p. 655-662. MR246603
24. [24] P. Sarnak, Commun. Math. Phys., t. 84, 1982, p. 377-401. Zbl0506.35074MR667408
25. [25] L.E. Thomas, C.E. Wayne, J. Math. Phys., t. 27, 1986, p. 71-75. Zbl0608.47018MR816416
26. [26] K. Yajima, J. Math. Soc. Japan, t. 29, 1977, p. 729-743. Zbl0356.47010MR470525
27. [27] E. Zehnder, Commun. Pure Appl. Math., t. 28, 1975, p. 91-148. Zbl0309.58006MR380867
28. [28] E. Zehnder, Commun. Pure Appl. Math., t. 29, 1976, p. 49-111. Zbl0334.58009MR426055

1. James S. Howland, Floquet operators with singular spectrum. I
2. Min-Jei Huang, On stability for time-periodic perturbations of harmonic oscillators