Periodic orbits and the homoclinic tangle in atom-surface chaotic scattering

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 56, Issue 1, 1997, Pages 378-389

  Guantes, R ^a   Borondo, F ^a   Miret Artes S ^b  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^b MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CALCULATIONS; CHAOS THEORY; CONVERGENCE OF NUMERICAL METHODS; COPPER; FRACTALS; HELIUM; MATHEMATICAL MODELS; SURFACE PHENOMENA;

HOMOCLINIC TANGLE; PERIODIC ORBITS; POINCARE SURFACE OF SECTION;

LATTICE VIBRATIONS;

EID: 0031191803     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.56.378     Document Type: Article

References (75)

1. M. Alagia, N. Balucani, L. Cartechini, P. Casavecchia, E. H. van Kleef, G G. Volpi, F J. Aoiz, L. Bañares, D W. Schwenke, T C. Allison, S L. Mielke, and G G. Truhlar, Science273, 1519 (1996).SCIEAS
2. J D. McClure, J. Chem. Phys.51, 1687 (1969); JCPSA6
3. 52, 2712 (1970);
4. 57, 2810 (1972);
5. 57, 2823 (1972);
6. D S. Sholl and R T. Skodje, Phys. Rev. Lett.75, 3158 (1995).PRLTAO
7. B. Eckhardt, Physica D33, 89 (1988); PDNPDT
8. U. Smilanski, in Chaos and Quantum Physics, edited by M.-J. Giannoni, A. Voros, and J. Zinn-Justin (Elsevier, Amsterdam, 1992), p. 371.
9. C. Jung, J. Phys. A19, 1345 (1986); JPHAC5
10. 20, 1719 (1987).
11. M J. Davis, J. Chem. Phys.83, 1016 (1985); JCPSA6
12. M J. Davis and S K. Gray, 84, 5389 (1986);
13. G P. Brivio and Z W. Gortel, Surf. Sci.261, 359 (1992); SUSCAS
14. G P. Brivio and M. Torri, Phys. Rev. B48, 4835 (1993); PRBMDO
15. G P. Brivio, M L. Rossi, M. Torri, and Z W. Gortel, Phys. Rev. Lett.76, 3376 (1996).PRLTAO
16. R A. Marcus, J. Chem. Phys.54, 3965 (1971); JCPSA6
17. 57, 4903 (1972);
18. W H. Miller, Adv. Chem. Phys.25, 69 (1974); ADCPAA
19. 30, 77 (1975).
20. C C. Rankin and W H. Miller, J. Chem. Phys.55, 3150 (1971).JCPSA6
21. N. Hill and V. Celli, Surf. Sci.75, 577 (1978).SUSCAS
22. S. Bleher, C. Grebogi, and E. Ott, Physica D46, 87 (1990); PDNPDT
23. M. Ding, C. Grebogi, E. Ott, and J. Yorke, Phys. Rev. A42, 7025 (1990); PLRAAN
24. R. Blümel and U. Smilanski, Physica D36, 111 (1989); PDNPDT
25. G. Troll and U. Smilanski, 35, 34 (1989);
26. J. Phys. A20, 5971 (1987); JPHAC5
27. C. Jung and H J. Scholz, 20, 3607 (1987).
28. (a) L. Gottdiener, Mol. Phys.29, 1585 (1975); MOPHAM
29. (b) N. Agmon, J. Chem. Phys.76, 1309 (1982); JCPSA6
30. (c) D W. Noid, S K. Gray, and S A. Rice, 84, 2649 (1986);
31. (d) J C. Polanyi and R J. Wolf, Ber. Bunsenges. Phys. Chem.86, 356 (1982); BBPCAX
32. (e) I. Burghardt and P. Gaspard, J. Phys. Chem.99, 2732 (1995). JPCHAX
33. (a) A. Tiyapan and C. Jaffé, J. Phys. Chem.99, 2765 (1993); JPCHAX
34. (b) 101, 10 393 (1994);
35. (c) 103, 5499 (1995).
36. (a) F. Borondo, C. Jaffé, and S. Miret-Artés, Surf. Sci.317, 211 (1994); SUSCAS
37. (b) R. Guantes, F. Borondo, C. Jaffé, and S. Miret-Artés, Int. J. Quantum Chem.52, 515 (1994); IJQCB2
38. (c) R. Guantes, F. Borondo, C. Jaffé, and S. Miret-Artés, Phys. Rev. B53, 14 117 (1996).PRBMDO
39. J M. Petit and M. Hénon, Icarus66, 536 (1986); ICRSA5
40. B. Eckhardt and H. Aref, Philos. Trans. R. Soc. London, Ser. A326, 655 (1988).PTRMAD
41. C. Lipp and C. Jung, J. Phys. A28, 6887 (1995); JPHAC5
42. B. Rückerl and C. Jung, 27, 6741 (1994).
43. (a) Z. Kovács and L. Wiesenfeld, Phys. Rev. E51, 5476 (1995); PLEEE8
44. (b) H. Wadi and L. Wiesenfeld, 55, 271 (1997).
45. K T. Hansen and A. Kohler, Phys. Rev. E54, 6214 (1996).PLEEE8
46. D. Gorse, B. Salanon, F. Fabre, A. Kara, J. Perreau, G. Armand, and J. Lapujoulade, Surf. Sci.47, 611 (1984).SUSCAS
47. B B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1983).
48. S. Wiggins, Introduction to Applied Non Linear Dynamical Systems and Chaos (Springer, New York, 1990).
49. (a) Y.-C. Lai, M. Ding, C. Grebogi, and R. Blümel, Phys. Rev. A46, 4661 (1992); PLRAAN
50. (b) C F. Hillermeier, R. Blümel, and U. Smilansky, 45, 3486 (1992);
51. (c) C. F. F. Karney, Physica D8, 360 (1983); PDNPDT
52. (d) J D. Meiss and E. Ott, 20, 387 (1986).
53. S. Benkadda, Y. Elskens, B. Ragot, and J T. Mendonca, Phys. Rev. Lett.72, 2859 (1994).PRLTAO
54. R. Guantes and F. Borondo (unpublished).
55. R S. MacKay, J D. Meiss, and I C. Percival, Physica D13, 55 (1984); PDNPDT
56. 27, 1 (1987);
57. D. Bensimon and L D. Kadanoff, 13, 82 (1984).
58. T. Horita, H. Hata, R. Ishizaki, and H. Mori, Prog. Theor. Phys.83, 1065 (1990); PTPKAV
59. M A. Sepulveda, R. Badii, and E. Pollak, Phys. Rev. Lett.63, 1226 (1989).PRLTAO
60. A. Weinstein, Invent. Math.20, 47 (1973); INVMBH
61. J. Moser, Commun. Pure Appl. Math.29, 727 (1976).CPAMAT
62. R. Prosmiti and S C. Farantos, J. Chem. Phys.103, 3299 (1995). JCPSA6
63. (a) R. DeVogelare, in Contributions to the Theory of Non Linear Oscillations, edited by S. Lefschetz (Princeton University Press, Princeton, 1958), Vol. IV, p. 53;
64. (b) J. Heagy and J M. Yuan, Phys. Rev. A41, 571 (1990); PLRAAN
65. (c) C. Jung and P H. Richter, Phys. Rev. A23, 2847 (1990). PLRAAN
66. (a)K R. Meyer, Trans. Am. Math. Soc.149, 95 (1970);
67. (b) M. A. M. de Aguiar, C P. Malta, M. Baranger, and K. T. R. Davies, Ann. Phys. (N.Y.)180, 167 (1987); APNYA6
68. (c) J.-M. Mao and J B. Delos, Phys. Rev. A45, 1746 (1992).PLRAAN
69. M. Tsuchiya, Ph.D. Thesis, West Virginia University, 1995.
70. G. L. da Silva Ritter, A. M. Ozorio de Almeida, and R. Douady, Physica D29, 181 (1987).PDNPDT
71. R S. MacKay, in Physics of Particle Accelerators, AIP Conf. Proc. No. 153 (AIP, New York, 1987).
72. A A. Zembekov, Phys. Rev. A42, 7163 (1990); PLRAAN
73. P. Veerman, Physica D29, 191 (1987).PDNPDT
74. P. Cvitanovic, B. Shraiman, and B. Söderberg, Phys. Scr.32, 263 (1985).PHSTBO
75. See, for example, T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1992), pp. 20 and 21.