Global analysis of periodic orbit bifurcations in coupled Morse oscillator systems: Time-reversal symmetry, permutational representations and codimension-2 collisions

Chaos

Volumn 9, Issue 4, 1999, Pages 819-840

  Tsuchiya, Masa ^a,b   Ezra, Gregory S ^a  

^a Department of Obstetrics Gynecology   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033473623     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166466     Document Type: Article

References (52)

1. H. Poincaré, New Methods of Celestial Mechanics (AIP, New York, 1993).
2. G. D. Birkhoff, Dynamical Systems (AMS, Providence, 1927).
3. R. S. MacKay and J. D. Meiss, Hamiltonian Dynamical Systems (Hilger, Berlin, 1987).
4. See, for example, P. Cvitanovic, Physica D 51, 138 (1991); 83, 109 (1995).
5. See, for example, P. Cvitanovic, Physica D 51, 138 (1991); 83, 109 (1995).
6. K. R. Meyer, Trans. Am. Math. Soc. 149, 95 (1970); K. R. Meyer and G. R. Hall, Introduction to Dynamical Systems and the N-body Problem (Springer, New York, 1992).
7. K. R. Meyer, Trans. Am. Math. Soc. 149, 95 (1970); K. R. Meyer and G. R. Hall, Introduction to Dynamical Systems and the N-body Problem (Springer, New York, 1992).
8. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer Verlag, Berlin, 1990).
9. M. S. Child, Semiclassical Mechanics with Molecular Applications (Oxford, New York, 1991); M. Brack and R. K. Bhaduri, Semiclassical Physics (Addison-Wesley, Reading, MA, 1997).
10. M. S. Child, Semiclassical Mechanics with Molecular Applications (Oxford, New York, 1991); M. Brack and R. K. Bhaduri, Semiclassical Physics (Addison-Wesley, Reading, MA, 1997).
11. H. Friedrich and D. Wintgen, Phys. Rep. 183, 37 (1989).
12. See, for example, G. Tanner, K. Richter, and J-M. Rost, Rev. Mod. Phys. (to appear), and references therein.
13. See, for example, R. Schinke, Photodissociation Dynamics (Cambridge University Press, Cambridge, UK, 1993), Chap. 8.
14. J. M. Mao and J. B. Delos, Phys. Rev. A 45, 1746 (1992).
15. H. S. Taylor, Acc. Chem. Res. 22, 263 (1989); S. C. Farantos, Int. Rev. Phys. Chem. 15, 345 (1996).
16. H. S. Taylor, Acc. Chem. Res. 22, 263 (1989); S. C. Farantos, Int. Rev. Phys. Chem. 15, 345 (1996).
17. G. S. Ezra, in Advances in Classical Trajectory Methods, Vol. 3, edited by W. L. Hase (JAI, New York, 1998).
18. P. Gaspard and P. van Ede van der Pals, J. Chem. Phys. 110, 5611 (1999).
19. R. S. MacKay, J. D. Meiss, and I. C. Percival, Physica D 28, 1 (1987).
20. M. J. Davis, J. Chem. Phys. 107, 4507 (1997).
21. M. J. Davis, Int. Rev. Phys. Chem. 14, 15 (1995).
22. See, for example, R. Marquardt, M. Quack, J. Stohner, and E. Sutcliffe, J. Chem. Soc., Faraday Trans. 2 86, 1173 (1986).
23. M. Tsuchiya and G. S. Ezra (work in progress).
24. L. Xiao and M. E. Kellman, J. Chem. Phys. 90, 6086 (1989); Z. Li, L. Xiao, and M. E. Kellman, ibid. 92, 2251 (1990); L. Xiao and M. E. Kellman, ibid. 93, 5805 (1990).
25. L. Xiao and M. E. Kellman, J. Chem. Phys. 90, 6086 (1989); Z. Li, L. Xiao, and M. E. Kellman, ibid. 92, 2251 (1990); L. Xiao and M. E. Kellman, ibid. 93, 5805 (1990).
26. L. Xiao and M. E. Kellman, J. Chem. Phys. 90, 6086 (1989); Z. Li, L. Xiao, and M. E. Kellman, ibid. 92, 2251 (1990); L. Xiao and M. E. Kellman, ibid. 93, 5805 (1990).
27. L. Xiao and M. E. Kellman, J. Chem. Phys. 93, 5821 (1990); J. Svitak, Z. Li, J. Rose, and M. E. Kellman, ibid. 102, 4340 (1995).
28. L. Xiao and M. E. Kellman, J. Chem. Phys. 93, 5821 (1990); J. Svitak, Z. Li, J. Rose, and M. E. Kellman, ibid. 102, 4340 (1995).
29. D. C. Rouben and G. S. Ezra, J. Chem. Phys. 103, 1375 (1995); G. S. Ezra, ibid. 104, 26 (1996).
30. D. C. Rouben and G. S. Ezra, J. Chem. Phys. 103, 1375 (1995); G. S. Ezra, ibid. 104, 26 (1996).
31. M. Joyeux, Chem. Phys. Lett. 247, 454 (1995).
32. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, Berlin, 1983).
33. R. DeVogelaere, in Contributions to the Theory of Nonlinear Oscillations, Vol. 4, edited by S. Lefschetz (Princeton University Press, NJ, 1958), p. 35.
34. J. M. Greene, AIP Conf. Proc. 57, 257 (1979).
35. J. M. Greene, R. S. MacKay, F. Vivaldi, and M. J. Feigenbaum, Physica D 3, 468 (1981).
36. M. Tsuchiya, Ph.D. thesis, West Virginia University, 1995; M. Tsuchiya and C. Jaffé, preprint.
37. M. Tsuchiya, Ph.D. thesis, West Virginia University, 1995; M. Tsuchiya and C. Jaffé, preprint.
38. T. Weston and M. S. Child, Chem. Phys. Lett. 262, 751 (1996). See also S. Cho and M. S. Child, Mol. Phys. 81, 447 (1994), Ref. 21.
39. T. Weston and M. S. Child, Chem. Phys. Lett. 262, 751 (1996). See also S. Cho and M. S. Child, Mol. Phys. 81, 447 (1994), Ref. 21.
40. D. A. Sadovskii, J. A. Shaw, and J. B. Delos, Phys. Rev. Lett. 75, 2120 (1995); D. A. Sadovskii and J. B. Delos, Phys. Rev. E 54, 2033 (1996).
41. D. A. Sadovskii, J. A. Shaw, and J. B. Delos, Phys. Rev. Lett. 75, 2120 (1995); D. A. Sadovskii and J. B. Delos, Phys. Rev. E 54, 2033 (1996).
42. K. R. Meyer, J. B. Delos, and J.-M. Mao, in Conservative Systems and Quantum Chaos, edited by L. M. Bates and D. L. Rod (American Mathematical Society, Providence, 1996).
43. H. Schomerus, J. Phys. A 31, 4167 (1998).
44. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers (Oxford University Press, New York, 1979).
45. J. Laskar, Physica D 67, 257 (1993); J. Laskar, C. Froeschlé, and A. Celletti, ibid. 56, 253 (1992).
46. J. Laskar, Physica D 67, 257 (1993); J. Laskar, C. Froeschlé, and A. Celletti, ibid. 56, 253 (1992).
47. L. E. Fried and G. S. Ezra, J. Chem. Phys. 86, 6270 (1987); M. E. Kellman, ibid. 93, 6630 (1990).
48. L. E. Fried and G. S. Ezra, J. Chem. Phys. 86, 6270 (1987); M. E. Kellman, ibid. 93, 6630 (1990).
49. Such dynamically defined surfaces of section have been used previously by C. Jaffé (private communication).
50. M. Tsuchiya and G. S. Ezra (unpublished).
51. M. V. Berry, J. P. Keating, and S. D. Prado, J. Phys. A 31, L245 (1998).
52. S. Tomsovic and E. J. Heller, Phys. Rev. E 47, 282 (1993).