Desingularization of Jacobi metrics and chaos in general relativity

Journal of Mathematical Physics

Volumn 40, Issue 7, 1999, Pages 3519-3539

  Szydłowski, Marek ^a  

^a JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033243803     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532905     Document Type: Article

References (62)

1. V. I. Arnold, Mathematical Methods in Classical Mechanics (Springer, New York, 1989).
2. C. P. Ong, Adv. Math. 15, 269 (1975).
3. M. Szydłowski, M. Heller, and W. Sasin, J. Math. Phys. 37, 346 (1996).
4. R. Arnowitt, S. Deser, and C. W. Misner, "The dynamics of general relativity," in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).
5. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, New York, 1971).
6. S. L. Bazański, J. Phys. A 27, 3221 (1994).
7. A. Wintner, The Analytical Foundations of Celestial Mechanics (Princeton University Press, Princeton, 1941).
8. H. Seifert, Math. Z. 51, 179 (1948).
9. V. V. Kozlov, Appl. Math. Mech. (in Chinese) 40, 399 (1976).
10. V. V. Kozlov, Vestn. Mosk. Inst. Mat. Mech. 5, 118 (1977).
11. V. V. Kozlov, Usp. Mat. Nauk 40, 33 (1985).
12. C. W. Misner, "Minisuperspace," in Magic Without Magic, edited by J. Klauder (Freeman, San Francisco, 1972).
13. B. S. DeWitt, "Space-time as a sheaf of geodesies in superspace," in Relativity, edited by M. Carmeli, S. I. Fickler, and L. Witten (Plenum, New York, 1970).
14. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer, New York, 1990).
15. H. G. Schuster, Deterministic Chaos, An Introduction (VCH, Weinheim, 1987).
16. R. F. Baierlein, D. H. Sharp, and J. A. Wheeler, Phys. Rev. 126, 1864 (1962).
17. J. B. Barbour and B. Bertotti, Proc. R. Soc. London, Ser. A 382, 295 (1982); J. B. Barbour, Class. Quantum Grav. 11, 2853 (1994).
18. J. B. Barbour and B. Bertotti, Proc. R. Soc. London, Ser. A 382, 295 (1982); J. B. Barbour, Class. Quantum Grav. 11, 2853 (1994).
19. K. Kuchar, Phys. Rev. D 4, 955 (1971).
20. M. Szydłowski, J. Math. Phys. 35, 1850 (1994); M. Szydłowski and A. Krawiec, Phys. Rev. D 53, 6893 (1996); 47, 5323 (1993); M. Szydłowski and M. Biesiada, ibid. 44, 2369 (1991).
21. M. Szydłowski, J. Math. Phys. 35, 1850 (1994); M. Szydłowski and A. Krawiec, Phys. Rev. D 53, 6893 (1996); 47, 5323 (1993); M. Szydłowski and M. Biesiada, ibid. 44, 2369 (1991).
22. M. Szydłowski, J. Math. Phys. 35, 1850 (1994); M. Szydłowski and A. Krawiec, Phys. Rev. D 53, 6893 (1996); 47, 5323 (1993); M. Szydłowski and M. Biesiada, ibid. 44, 2369 (1991).
23. M. Szydłowski, J. Math. Phys. 35, 1850 (1994); M. Szydłowski and A. Krawiec, Phys. Rev. D 53, 6893 (1996); 47, 5323 (1993); M. Szydłowski and M. Biesiada, ibid. 44, 2369 (1991).
24. R. Abraham and J. E. Marsden, Foundations of Mechanics (Cummings, Massachusetts, 1978); C. Lanczos, The Variational Principles of Mechanics (University of Toronto Press, Toronto, 1957); A. J. McConnell, Application of Tensor Analysis (Dover, New York, 1957); E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge University Press, Cambridge, 1959); J. L. Synge, Philos. Trans. R. Soc. London, Ser. A 226, 91 (1926); J. Moser, Commun. Pure Appl. Math. 23, 609 (1970).
25. R. Abraham and J. E. Marsden, Foundations of Mechanics (Cummings, Massachusetts, 1978); C. Lanczos, The Variational Principles of Mechanics (University of Toronto Press, Toronto, 1957); A. J. McConnell, Application of Tensor Analysis (Dover, New York, 1957); E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge University Press, Cambridge, 1959); J. L. Synge, Philos. Trans. R. Soc. London, Ser. A 226, 91 (1926); J. Moser, Commun. Pure Appl. Math. 23, 609 (1970).
26. R. Abraham and J. E. Marsden, Foundations of Mechanics (Cummings, Massachusetts, 1978); C. Lanczos, The Variational Principles of Mechanics (University of Toronto Press, Toronto, 1957); A. J. McConnell, Application of Tensor Analysis (Dover, New York, 1957); E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge University Press, Cambridge, 1959); J. L. Synge, Philos. Trans. R. Soc. London, Ser. A 226, 91 (1926); J. Moser, Commun. Pure Appl. Math. 23, 609 (1970).
27. R. Abraham and J. E. Marsden, Foundations of Mechanics (Cummings, Massachusetts, 1978); C. Lanczos, The Variational Principles of Mechanics (University of Toronto Press, Toronto, 1957); A. J. McConnell, Application of Tensor Analysis (Dover, New York, 1957); E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge University Press, Cambridge, 1959); J. L. Synge, Philos. Trans. R. Soc. London, Ser. A 226, 91 (1926); J. Moser, Commun. Pure Appl. Math. 23, 609 (1970).
28. R. Abraham and J. E. Marsden, Foundations of Mechanics (Cummings, Massachusetts, 1978); C. Lanczos, The Variational Principles of Mechanics (University of Toronto Press, Toronto, 1957); A. J. McConnell, Application of Tensor Analysis (Dover, New York, 1957); E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge University Press, Cambridge, 1959); J. L. Synge, Philos. Trans. R. Soc. London, Ser. A 226, 91 (1926); J. Moser, Commun. Pure Appl. Math. 23, 609 (1970).
29. R. Abraham and J. E. Marsden, Foundations of Mechanics (Cummings, Massachusetts, 1978); C. Lanczos, The Variational Principles of Mechanics (University of Toronto Press, Toronto, 1957); A. J. McConnell, Application of Tensor Analysis (Dover, New York, 1957); E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge University Press, Cambridge, 1959); J. L. Synge, Philos. Trans. R. Soc. London, Ser. A 226, 91 (1926); J. Moser, Commun. Pure Appl. Math. 23, 609 (1970).
30. M. Pettini, Phys. Rev. E 47, 826 (1993).
31. L. Casetti, C. Clementi, and M. Pettini, Phys. Rev. E 54, 5969 (1996); M. Cerruti-Sola and M. Pettini, ibid. 53, 179 (1996); 51, 53 (1995); L. Casetti, R. Livi, and M. Pettini, Phys. Rev. Lett. 74, 375 (1995).
32. L. Casetti, C. Clementi, and M. Pettini, Phys. Rev. E 54, 5969 (1996); M. Cerruti-Sola and M. Pettini, ibid. 53, 179 (1996); 51, 53 (1995); L. Casetti, R. Livi, and M. Pettini, Phys. Rev. Lett. 74, 375 (1995).
33. L. Casetti, C. Clementi, and M. Pettini, Phys. Rev. E 54, 5969 (1996); M. Cerruti-Sola and M. Pettini, ibid. 53, 179 (1996); 51, 53 (1995); L. Casetti, R. Livi, and M. Pettini, Phys. Rev. Lett. 74, 375 (1995).
34. L. Casetti, C. Clementi, and M. Pettini, Phys. Rev. E 54, 5969 (1996); M. Cerruti-Sola and M. Pettini, ibid. 53, 179 (1996); 51, 53 (1995); L. Casetti, R. Livi, and M. Pettini, Phys. Rev. Lett. 74, 375 (1995).
35. J. C. Larsen, J. Geom. Phys. 9, 3 (1992).
36. V. V. Kozlov, Dokl. Akad. Nauk SSSR 249, 1299 (1979); S. Bolotin, J. Math. Phys. 1, 275 (1994).
37. V. V. Kozlov, Dokl. Akad. Nauk SSSR 249, 1299 (1979); S. Bolotin, J. Math. Phys. 1, 275 (1994).
38. J. D. Barrow, Phys. Rep. 85, 1 (1982); V. A. Belinski, E. M. Lifszyc, and I. M. Khalatnikov, Adv. Phys. 19, 525 (1970).
39. J. D. Barrow, Phys. Rep. 85, 1 (1982); V. A. Belinski, E. M. Lifszyc, and I. M. Khalatnikov, Adv. Phys. 19, 525 (1970).
40. C. Lanczos, The Variational Principles of Mechanics (Toronto University Press, Toronto, 1949); J. L. Synge, Classical Dynamics, Handbuch der Physik III/I, edited by S. Flüge/Marburg (Springer, Berlin, 1960).
41. C. Lanczos, The Variational Principles of Mechanics (Toronto University Press, Toronto, 1949); J. L. Synge, Classical Dynamics, Handbuch der Physik III/I, edited by S. Flüge/Marburg (Springer, Berlin, 1960).
42. N. J. Cornish and J. J. Levin, Phys. Rev. D 53, 3022 (1996); Phys. Rev. Lett. 78, 998 (1997).
43. N. J. Cornish and J. J. Levin, Phys. Rev. D 53, 3022 (1996); Phys. Rev. Lett. 78, 998 (1997).
44. L. P. Eisenhart, Ann. Math. 30, 591 (1929).
45. M. A. Abramowicz, B. Carter, and J. P. Lasota, Gen. Relativ. Gravit. 20, 1173 (1988); 20, 275 (1988).
46. M. A. Abramowicz, B. Carter, and J. P. Lasota, Gen. Relativ. Gravit. 20, 1173 (1988); 20, 275 (1988).
47. M. P. Ryan Jr. and S. M. Waller, 1997, gr-qc/9709012.
48. O. Bogoyavlenskii, Methods in the Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics (Springer, New York, 1985).
49. G. F. R. Ellis, A. Sumeruk, and C. Hellaby, Class. Quantum Grav. 9, 1535 (1992).
50. V. Szebehely, Celest. Mech. 34, 49 (1984).
51. D. V. Fursaev and S. N. Solodukhin, Phys. Rev. D 52, 2133 (1995); D. D. Sokolov and A. A. Starobinsky, D A SSSR 22, 312 (1997).
52. D. V. Fursaev and S. N. Solodukhin, Phys. Rev. D 52, 2133 (1995); D. D. Sokolov and A. A. Starobinsky, D A SSSR 22, 312 (1997).
53. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
54. M. Szydłowski, J. Math. Phys. 35, 1850 (1994); M. Szydłowski and A. Krawiec, Phys. Rev. D 53, 6893 (1996).
55. M. Szydłowski, J. Math. Phys. 35, 1850 (1994); M. Szydłowski and A. Krawiec, Phys. Rev. D 53, 6893 (1996).
56. B. DeWitt, Phys. Rev. 160, 1113 (1967).
57. H. Goenner, E. W. Grafarend, and R. J. You, Manuscr. Geodetica 19, 339 (1994).
58. M. Szydłowski, Contemp. Math. 203, 289 (1997).
59. E. Calzetta and C. E. Hasi, Class. Quantum Grav. 10, 1825 (1993).
60. A. H. Guth and S.-Y. Pi, Phys. Rev. D 32, 257 (1985).
61. H. Varvoglis and D. Papadopoulos, Astron. Astrophys. 261, 664 (1992).
62. S. Blanco, A. Costa, and O. A. Rosso, Gen. Relat. Grav. 27, 1295 (1995).