Periodic orbits near bifurcations of codimension two: Classical mechanics, semiclassics and stokes transitions

Journal of Physics A: Mathematical and General

Volumn 31, Issue 18, 1998, Pages 4167-4196

  Schomerus, Henning ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001010199     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/31/18/008     Document Type: Article

References (42)

1. Gutzwiller M C 1971 J. Math. Phys. 12 343
2. Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics ( New York: Springer)
3. Tabor M 1983 Physica 6 D 195
4. Junker G and Leschke H 1992 Physica 56 D 135
5. Berry M V and Tabor M 1976 Proc. R. Soc. A 349 101
6. Berry M V and Tabor M 1977 J. Phys. A: Math. Gen. 10 371
7. Ozorio de Almeida A M and Hannay J H 1987 J. Phys. A: Math. Gen. 20 5873
8. Ozorio de Almeida A M 1988 Hamiltonian Systems: Chaos and Quantization ( Cambridge: Cambridge University Press)
9. Kuś M, Haake F and Delande D 1993 Phys. Rev. Lett. 71 2167
10. Sieber M 1996 J. Phys. A: Math. Gen. 29 4715
11. Schomerus H and Sieber M 1997 J. Phys. A: Math. Gen. 30 4537
12. Sieber M and Schomerus H 1998 J. Phys. A: Math. Gen. 31 165
13. Meyer K R 1970 Trans. Am. Math. Soc. 149 95
14. Bruno A D 1970 Math. USSR Sbornik 12 271
15. Bruno A D 1972 Inst. Prikl. Mat. Akad. Nauk SSSR Preprint No 18 Moskau (in Russian)
16. Rimmer R J Memoirs of the AMS vol 272 (Providence, RI: American Mathematical Society)
17. Golubitsky M and Stewart I 1987 Physica 24 D 391
18. de Aguiar M A M, Malta C P, Baranger M and Davies K T R Ann. Phys., NY 180 167
19. de Aguiar M A M and Malta C P 1988 Physica 30 D 413
20. Ozorio de Almeida A M and de Aguiar MAM 1990 Physica 41 D 391
21. Schomerus H 1997 Europhys. Lett. 38 423
22. Schomerus H and Haake F 1997 Phys. Rev. Lett. 79 1022 a more detailed exposition is in preparation
23. Sadovskií D A, Shaw J A and Delos J B 1995 Phys. Rev. Lett. 75 2120
24. Sadovskií D A and Delos J B 1996 Phys. Rev. E 54 2033
25. Poincaré H 1957 New Methods of Celestial Mechanics vol 3 ( New York: Dover)
26. Birkhoff G D 1927 Dynamical Systems ( New York: American Mathematical Society)
27. Deprit A 1969 Celest. Mech. 1 12
28. Arnol'd V I 1988 Geometrical Methods of the Theory of Ordinary Differential Equations (Series of Comprehensive Studies in Mathematics 250) ( New York: Springer)
29. Meyer K R 1986 Contemp. Math. 56 373
30. Main J and Wunner G 1997 Phys. Rev. A 55 1743
31. Copson E T 1965 Asymptotic Expansions ( Cambridge: Cambridge University Press)
32. Dingle R B 1973 Asymptotic Expansions: Their Derivation and Interpretation ( London: Academic)
33. Fedoryuk M V 1989 Asymptotic Methods in Analysis, Analysis I (Encyclopaedia of Mathematical Sciences 13) ed R V Gamkrelidze (Berlin: Springer) pp 33-191
34. Berry M V 1989 Proc. R. Soc. A 422 7
35. Boasman P A and Keating J P 1995 Proc. R. Soc. A 449 629
36. Meyer K R and Hall G R 1992 Introduction to Hamiltonian Dynamical Systems and the N-body Problem (Applied Mathematical Sciences 90) ( New York: Springer)
37. Mao J M and Delos J B 1992 Phys. Rev. A 45 1746
38. Tomsovic S, Grinberg M and Ullmo D 1995 Phys. Rev. Lett. 75 4346
39. Ullmo D, Grinberg M and Tomsovic S 1996 Phys. Rev. E 54 136
40. Wright F J 1980 J. Phys. A: Math. Gen. 13 2913
41. Poston T and Stewart I N 1978 Catastrophe Theory and its Applications ( London: Pitman)
42. Berry M V and Upstill C 1980 Progress in Optics vol 8, ed E Wolf (Amsterdam: North-Holland) pp 257-346