Normal Forms and Complex Periodic Orbits in Semiclassical Expansions of Hamiltonian Systems

Annals of Physics

Volumn 275, Issue 1, 1999, Pages 54-112

  Leboeuf P ^a   Mouchet, A ^b  

^a UNIVERSITÉ PARIS SUD   (France)

^b Lab Mathematiques de Phys Theor ^*  (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347874971     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1006/aphy.1999.5916     Document Type: Article

References (58)

1. Abraham R., Marsden J. E. Foundations of Mechanics. 1985;Addison-Wesley, New York.
2. Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations. Grundlehren Math. Wiss. 250:1988;Springer-Verlag, New York.
3. Arnold V. I., Avez A. Problèmes ergodiques de la Mécanique classique. Monographies Internationales de Mathématiques Modernes. 9:1967;Gauthier-Villars, Paris.
4. Balian R., Bloch C. Ann. Phys. 85:1974;514.
5. M. V. Berry, in Topics in Nonlinear Dynamics - A Tribute to Sir Edward Bullard (J. Siebe, Ed.), Vol. 46, pp. 16-120; reprint, in "Hamiltonian Dynamical Systems," Hilger, Bristol, 1987.
6. M. V. Berry, in Topics in Nonlinear Dynamics - A Tribute to Sir Edward Bullard (J. Siebe, Ed.), Vol. 46, pp. 16-120; reprint, in "Hamiltonian Dynamical Systems," Hilger, Bristol, 1987.
7. Berry M. V., Howls C. J. Proc. R. Soc. London Ser. A. 434:1991;657.
8. Berry M. V., Howls C. J. Proc. R. Soc. London Ser. A. 447:1994;527.
9. Birkhoff G. D. Dynamical Systems. American Mathematical Society Colloquium Publications. 9:1927;Amer. Math. Soc. New York.
10. Birkhoff G. D. George David Birkhoff, Collected Mathematical Papers. 1950;Amer. Math. Soc. New York.
11. Bogomolny E. B. Nonlinearity. 5:1992;805.
12. Bogomolny E. B., Fateev V. A., Lipatov L. N. Soviet Sc. Rev. Phys. Rev. 2:1980;247.
13. Bohigas O., Boosé D., Egydio de Carvalho R., Marvulle V. Nuclear Phys. A. 560:1993;197.
14. Bruno A. Math. USSR-Sb. 12:1970;271.
15. Carruthers P., Nieto M. M. Rev. Mod. Phys. 40:1968;411.
16. Cartier P., Voros A. C.R. Acad. Sci. Paris Sér. I Math. 307:1988;143.
17. Cherry T. M. Proc. London Math. Soc. (2). 27:1927;151.
18. Cherry T. M. Proc. London Math. Soc. (2). 26:1927;211.
19. Cherry T. M. Philos. Trans. R. Soc. London Ser. A. 227:1928;137.
20. Creagh S. C., Whelan N. D. Phys. Rev. Lett. 77:1996;4975.
21. Cushman R., Deprit A., Mosak R. J. Math. Phys. 24:1983;2102.
22. De Agular M. A. M., Malta C. P., Baranger M., Davies K. T. R. Ann. Phys. 180:1987;167.
23. Doron E., Frischat S. D. Phys. Rev. Lett. 75:1995;3661.
24. Floquet G. Ann Sci. École Norm. Sup. (2). 12:1883;47.
25. Frischat S., Doron E. Phys. Rev. E. 57:1998;1421.
26. Gustavson F. G. Astron. J. 71:1966;670.
27. Gutzwiller M. C. Chaos in Classical and Quantum Mechanics. Interdisciplinary Applied Mathematics. 1:1990;Springer-Verlag, New York.
28. Henrard J. Celestial Mech. 3:1970;107.
29. Howls C. J. Exponential Asymptotics. 1991;University of Bristol, Bristol.
30. Itzykson C., Zuber J.-B. Quantum Field Theory. International Series in Pure and Applied Physics. 1980;McGraw-Hill, New York.
31. Kuś M., Haake F., Delande D. Phys. Rev. Lett. 71:1993;2167.
32. Lebœuf P., Mouchet A. Phys. Rev. Lett. 73:1994;1360.
33. Lin W., Ballentine L. Phys. Rev. Lett. 65:1990;2927.
34. Mackay R. S., Meiss J. D. Hamiltonian Dynamical Systems. 1987;Hilger, Bristol.
35. Meyer K. R. Trans. Amer. Math. Soc. 149:1970;95.
36. Meyer K. R. Trans. Amer. Math. Soc. 154:1971;227.
37. Meyer K. R. Contemp. Math. 56:1986;373.
38. Meyer K. R., Hall G. H. Introduction to Hamiltonian Dynamical Systems and the N-Body Problem. Applied Mathematical Sciences. 90:1992;Springer-Verlag, New York.
39. Miller W. H. J. Chem. Phys. 53:1970;1949.
40. Moser J. K. Comm. Pure Appl. Math. 9:1956;673.
41. Ozorio de Almeida A. M., Hannay J. H. J. Phys. A. 20:1987;5873.
42. Poincaré H. Les méthodes nouvelles de la mécanique céleste. 1957;Dover, New York.
43. Poston T., Stewart I. Catastrophe Theory and Its Applications. 1978;Pitman, London.
44. Prosen T. J. Phys. A. 28:1995;4133.
45. Schomerus H., Sieber M. J. Phys. A. 30:1997;4537.
46. Schulman L. S. Techniques and Applications of Path Integration. 1981;Wiley, New York.
47. Sieber M. J. Phys. A. 29:1996;4715.
48. Sieber M. J. Phys. A. 30:1997;4563.
49. Tabor M. Phys. D. 6:1983;195.
50. Tomsovic S., Grinberg M., Ullmo D. Phys. Rev. Lett. 75:1995;4346.
51. Tomsovic S., Ullmo D. Phys. Rev. E. 50:1994;145.
52. Turnbull H. W., Aitken A. C. An Introduction to the Theory of Canonical Matrices. 1961;Dover, New York.
53. Voros A. Ann. Inst. H. Poincaré Phys. Théor. 39:1983;211.
54. Voros A. Progr. Theoret. Phys. Suppl. 116:1994;17.
55. Voros A. J. Phys. A. 27:1994;4653.
56. Whittaker E. T. A Treatise on the Analytic Dynamics of Particles and Rigid Bodies. 1964;Cambridge Univ. Press, Cambridge.
57. Williamson J. Amer. J. Math. 58:1936;141.
58. Shudo A., Ikesa K. S. Phys. D. 115:1998;234.