Topology of high-dimensional chaotic scattering

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

Volumn 62, Issue 5, 2000, Pages 6421-6428

  Lai, Ying Cheng ^a   de Moura, Alessandro P S ^b   Grebogi, Celso ^b,c  

^a Arizona State University   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

^c Bldg 142   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; DEGREES OF FREEDOM (MECHANICS); FRACTALS; MOLECULAR STRUCTURE; PHASE SPACE METHODS; SCATTERING; SET THEORY;

CHAOTIC SCATTERING; METAMORPHOSIS DYNAMICS; SCATTERING FUNCTIONS;

TOPOLOGY;

EID: 0034318667     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.6421     Document Type: Article

References (34)

1. See, for example, R. Blümel, Chaos 3, 683 (1993).
2. See, for example, P. T. Boyd and S. L. W. McMillan, Chaos 3, 507 (1993).
3. See, for example, B. Eckhardt and H. Aref, Trans. Soc. R. London A 326, 655 (1988)
4. E. Ziemniak, C. Jung, and T. Tél, Physica D 76, 123 (1994)
5. Á. Péntek, T. Tél, and Z. Toroczkai, J. Phys. A 28, 2191 (1995).
6. See, for example, D. W. Noid, S. Gray, and S. A. Rice, J. Chem. Phys. 84, 2649 (1986)
7. Z. Kovács and L. Wiesenfeid, Phys. Rev. E 51, 5476 (1995).
8. See, for example, R. A. Jalabert, H. U. Baranger, and A. D. Stone, Phys. Rev. Lett. 65, 2442 (1990)
9. Phys. Rev. Lett.Y.-C. Lai, R. Blümel, E. Ott, and C. Grebogi, 68, 3491 (1992)
10. C. M. Marcus, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, Chaos 3, 643 (1993).
11. T. Tél, in Directions in Chaos, edited by Bai-lin Hao (World Scientific, Singapore, 1990), Vol. 3
12. in STATPHYS 19, edited by Bai-lin Hao (World Scientific, Singapore, 1996).
13. Chaos Focus Issue 3 (4) (1993).
14. S. Bleher, C. Grebogi, and E. Ott, Physica D 46, 87 (1990)
15. K.-C. Lai, Phys. Rev. E 60, R6283 (1999).
16. M. Ding, C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. A 42, 7025 (1990).
17. Y.-C. Lai and C. Grebogi, Phys. Rev. E 49, 3761 (1994).
18. Q. Chen, M. Ding, and E. Ott, Phys. Lett. A 145, 93 (1990)
19. D. Sweet, E. Ott, and J. A. Yorke, Nature (London) 399, 315 (1999).
20. P. M. Morse, Phys. Rev. 34, 57 (1929)
21. Phys. Rev.D. ter Haar, 70, 222 (1946).
22. See, for example, J. Heagy and J. M. Yuan, Phys. Rev. A 41, 571 (1990), and references therein.
23. L. Verlet, Phys. Rev. 159, 98 (1967).
24. Previous studies of planar scattering systems showed that chaotic scattering can arise when the particle energy is decreased through (Formula presented) the height of the potential hills 8. This energy regime, however, is physically unrealistic in situations such as particle scattering by molecules, where the centers of the potential hills are classically impenetrable.
25. S. W. McDonald, C. Grebogi, E. Ott, and J. A. Yorke, Physica D 17, 125 (1985).
26. For a fixed energy, the uncertainty fraction (Formula presented) is computed by using 40 values of ε in the range (Formula presented) For each ε, pairs of initial conditions are chosen randomly until the number of uncertain ones reaches 200. The computation was extremely intensive and was done on a 16-node Beowulf supercomputer.
27. P. Gaspard and S. A. Rice, J. Chem. Phys. 90, 2225 (1989).
28. J. Hocking and G. Young, Topology (Addison-Wesley, Reading, MA, 1961). For Wada basins in dissipative chaotic systems, see, for
29. J. Kennedy and J. A. Yorke, Physica D 51, 213 (1991).
30. L. Poon, J. Campos, E. Ott, and C. Grebogi, Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, 251 (1996)
31. Z. Toroczkai, G. Károlyi, Á. Péntek, T. Tél, C. Grebogi, and J. Yorke, Physica A 239, 233 (1997)
32. M. A. Sanjuan, J. Kennedy, C. Grebogi, and J. A. Yorke, Chaos 3, 125 (1997)
33. J. Kennedy, M. A. Sanjuan, J. A. Yorke, and C. Grebogi, Top. Appl. Phys. 94, 207 (1999).
34. H. E. Nusse and J. A. Yorke, Physica D 36, 137 (1989).