Symbolic dynamics and periodic orbits for the cardioid billiard

Journal of Physics A: Mathematical and General

Volumn 30, Issue 6, 1997, Pages 1991-2020

  Backer A ^a,c   Dullin, H R ^b  

^a UNIVERSITY OF HAMBURG   (Germany)

^b UNIVERSITY OF BREMEN   (Germany)

^c UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039269070     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/30/6/023     Document Type: Article

References (55)

1. Alekseev V and Yakobson M 1981 Phys. Rep. 75 287-325
2. Gutzwiller M C 1973 J. Math. Phys. 14 139-52
3. Gutzwiller M C 1976 J. Math. Phys. 18 806-23
4. Giannoni M J and Ullmo D 1990 Physica 41D 371-90
5. Morita T 1991 Trans. Am. Math. Soc. 325 819-28
6. Morita T 1994 Ergod. Theor. Dynam. Sys. 14 599-619
7. Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics (New York: Springer)
8. Cvitanovíc P, Gunaratne G H and Procaccia I 1988 Phys. Rev. A 38 1503-20
9. Hansen K T 1992 Phys. Lett. A 165 100-4
10. Hansen K T 1993 Nonlinearity 6 753-69
11. Hansen K T 1993 Nonlinearity 6 771-8
12. Hansen K T 1995 Phys. Rev. E 51 1838-44
13. Hansen K T and Cvitanović P 1995 Symbolic dynamics and Markov partitions for the stadium billiard Preprint chao-dyn/9502005
14. Ullmo D and Giannoni M J 1995 Physica 84D 329-56
15. Tanner G, Hansen K T and Main J 1996 Nonlinearity 9 1641-70
16. Wojtkowski W 1986 Commun. Math. Phys. 105 391-414
17. Szaśz D 1992 Commun. Math. Phys. 145 595-604
18. Markarian R 1993 Nonlinearity 6 819-41
19. Chernov N I and Haskell C 1996 Ergod. Theor. Dynam. Sys. 16 19-44
20. Robnik M 1983 J. Phys. A: Math. Gen. 16 3971-86
21. Robnik M 1984 J. Phys. A: Math. Gen. 17 1049-74
22. Prosen T and Robnik M 1993 J. Phys. A: Math. Gen. 26 2371-87
23. Bäcker A, Steiner F and Stifter P 1995 Phys. Rev. E 52 2463-72
24. Bäcker A 1995 Spektrale Statistiken des quantisierten Kardioid-Billards Diploma Thesis Universität Hamburg
25. Bruus H and Whelan ND 1996 Nonlinearity 9 1023-47
26. Dullin H R, Richter P H and Wittek A 1996 Chaos 6 43-58
27. Sieber M and Steiner F 1990 Physica 44D 248-66
28. Wittek A 1991 Die Quantenmechanik eines nichtintegrablen Systems PhD Thesis Universität Bremen
29. Meiss J D 1992 Rev. Mod. Phys. 64 795-848
30. MacKay R S and Meiss J D 1983 Phys. Lett. 98A 92-4
31. Bunimovich L A 1995 Chaos 5 349
32. Richter P H, Scholz H-J and Wittek A 1990 Nonlinearity 3 45-67
33. Jung C and Richter PH 1990 J. Phys. A: Math. Gen. 23 2847-66
34. Liverani C and Wojtkowski M P 1995 Dynamics Reported. Expositions in Dynamical Systems vol 4, ed C K R T Jones, U Kirchgraber and H O Walther (Berlin: Springer) pp 130-202
35. Hansen K T 1993 Nonlinearity 6 753-69
36. Arnold V I and Avez A 1968 Ergodic Problems of Classical Mechanics (New York: Benjamin)
37. Sieber M 1991 The hyperbola billiard: a model for the semiclassical quantization of chaotic systems PhD Thesis Universität Hamburg, DESY Report DESY 91-030
38. Creagh S C, Robbins J M and Littlejohn R G 1990 Phys. Rev. A 42 1907-22
39. Robbins J M 1989 Phys. Rev. A 40 2128-36
40. Sieber M, Smilansky U, Creagh S C and Littlejohn R G 1993 J. Phys. A: Math. Gen. 26 6217-30
41. Alonso D and Gaspard P 1994 J. Phys. A: Math. Gen. 27 1599-607
42. Aurich R, Hesse T and Steiner F 1995 Phys. Rev. Lett. 74 4408-11
43. Vattay G, Wirzba A and Rosenqvist P E 1994 Phys. Rev. Lett. 73 2304-8
44. Pavloff N and Schmit C 1995 Phys. Rev. Lett. 75 61-4 (erratum 1995 Phys. Rev. Lett. 75 3779)
45. Primack H, Schanz H, Smilansky U and Ussishkin I 1996 Phys. Rev. Lett. 76 1615-18
46. Whelan N D 1996 Phys. Rev. Lett. 76 2605-8
47. Artuso R, Aurell E and Cvitanović P 1990 Nonlinearity 3 325-59
48. Benettin G and Strelcyn J-M 1978 Phys. Rev. A 17 773-85
49. Eckmann J-P and Ruelle D 1985 Rev. Mod. Phys. 57 617-56
50. Grebogi C, Ott E and Yorke J A 1988 Phys. Rev. A 37 1711-24
51. Gaspard P and Alonso D 1992 Phys. Rev. A 45 8383-97
52. Hannay J H and Ozorio De Almeida A M 1984 J. Phys. A: Math. Gen. 17 3429-40
53. Harayama T and Shudo A 1992 J. Phys. A: Math. Gen. 25 4595-611
54. Szeredi T and Goodings D A 1993 Phys. Rev. E 48 3518-28
55. Aurich R and Marklof J 1996 Physica 92D 101-29