The chaotic mixmaster and the suppression of chaos in scalar-tensor cosmologies

General Relativity and Gravitation

Volumn 36, Issue 12, 2004, Pages 2635-2672

  Menza, Laurent Di ^a   Lehner, Thierry ^b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b UNIVERSITÉ PARIS DIDEROT   (France)

Author keywords

Chaos; General relativity; Mixmaster universe; Scalar tensor field

Indexed keywords

EID: 23944512126     PISSN: 00017701     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:GERG.0000048963.46730.c0     Document Type: Article

References (48)

1. Belinskii, V.A., Khalatnikov, L.M., and Lifshitz, E.M. (1970). Adv. Phys. 19, 525. (and references therein to their former papers starting in 1962).
2. Rugh, S. E. (1990). Phys. Lett. A 147, 353.
3. Elskens, Y. (1987). Class. Quant. Grav, 4, 161;
4. Elskens, Y. (1987). Nucl. Phys. B 290, 111;
5. Elskens, Y. (1987). J. Stat. Phys. 48, 1269.
6. Belinskii, V. A. and Khalatnikov, L. M. (1973). Sov. Phys. JETP 36, 591.
7. Barrow, J. D. and Stein-Schabes J. (1985). Phys. Rev. D 32 (6), 1595-1596.
8. Arnowitt, R. and Deser, S. (1959). Phy. Rev. 113, 745-750;
9. Arnowitt, R., Deser, S., and Misner, C. W. (1959). Phy.Rev. 116, 1322-1330;
10. Arnowitt, R. and Deser, S. (1960). Misner, C. W. (1962). Phys. Rev. 117, 1595-1602;
11. Arnowitt, R., Deser, S., and Misner, C. W. (1962). In Gravitation: An Introduction to Current Research, L. Witten (Ed.), Wiley, New York, Chap. 7, pp. 227-265.
12. Matzner, R. A., Ryan, M. P., and Toton, E. T. (1973). Nuovo Cim. B 14, 161-172.
13. Nariai, H. (1972). Prog. Theor. Phy. 47, 6.
14. Lifshitz, E. M., Khalatnikov, I. M., Sinai, Ya. G., Khanin, K. M., and Schur, L. N. (1983). Sov. Phys. JETP Lett. 38, 91.
15. Barrow, J. D. (1981). Phys. Rev. Lett. 46, 963-966.
16. Scheen, C. (1999). PhD thesis, Liege University.
17. Musette, M. and Conte, R. (1995). Phys. Lett. A 206, 340-346.
18. Misner, C. W. (1969). Phys. Rev. Lett.;
19. Misner, C. W. (1969). Phys. Rev. 186(5), 1319.
20. Barrow, J. D. and Tipler, F. J. (1979). Phys. Rep. 56, 371.
21. Barrow, J. D. (1982). Phys. Rep. 85, 1.
22. Berger, B. K. (2001). Phys. Rev. D 64, 084006.
23. Weaver, M., Isenberg, J., and Berger, B. K. (1998). Phys. Rev. Lett. 80, 2984-2987.
24. Chernoff, D. F. and Barrow, J. D. (1983). Phys. Rev. Lett. 50, 134.
25. Barrow, J. D. (1984). In Classical General Relativity, W. Bonnor, J. Islam, and M. A. H. Mac-Callum, Eds. Cambridge University Press, Cambridge, UK pp. 25-41.
26. Hobill, D., Burd, A., and Coley, A. (1991). Deterministic Chaos in General Relativity Plenum, New York.
27. Wainwright, J. and Ellis, G. F. R. (1997). Dynamical Systems in Cosmology, Cambridge University Press, Cambridge, UK.
28. Cornish, N. J. and Levin, J. J. (1997). Phys. Rev. D 55(12), 7489-7510.
29. Barrow, J. D. and Dabrowski, M. P. (1998). Phys. Rev. D 57(12), 7204-7222.
30. Damour, T. and Henneaux, M. (2000). Phys. Rev. Lett. 85, 920;
31. Damour, T., and Henneaux, M. (2001). Phys. Rev. Lett. 86, 4749.
32. Damour, T., Henneaux, M., Rendall, A. D., and Weaver, M. (2002). "Kasner-like behaviour for subcritical Einstein-matter systems," gr-qc/0202069.
33. Andersson, L. and Rendall, A. D. (2001). "Quiescent Cosmological Singularities." Commun. Math. Phys. 218, 479-511. gr-qc/0001047 v1 (01/17/00).
34. Ringström, H. (2001). "Ann. Henri Poincare 2, 405-500.
35. Arnold, V. I. (Ed.) (1993). Encyclopedia of Mathematics Dynamical systems III: Mathematical Aspects of Classical and Celetial Mechanics Springer, Berlin.
36. Zehnder, E. (1979). Commun. Pure Appl. Math. 26.
37. Kantowski, R. and Sachs, S. K. (1966). J. Math. Phys. 7, 443-446.
38. Landau, L. D. and Lifshitz, E. M. (1975). "The Classical Theory of Fields, Pergamon Press, Oxford.
39. Bunimovitch, L. A. (1974). Funktsional'nyl Analiz Ego Prilozheniya, 6(3), 73-74.
40. Bunimovitch, L. A. (1983). In Billards and Other Hyperbolic Systems, in Dynamical Systems Ergodic theory and Applications, Frohlich, J., Novikov, S. P., and Ruelle, D. (Eds), Springer, Berlin.
41. Bunimovitch, L. A. (1990). Commun. Math. Phys. 130, 599.
42. Bunimovitch, L. A., Sinai, Y. A. G., and Chernov, N. I. (1991). Russ. Math. Survey 46 (4), 47.
43. Misner, C. W. (1994). Deterministic Chaos in General Relativity, Hobill, D., Burd, A., and Coley, A. (Eds.) Plenum, New York, pp. 317-328.
44. Rugh, S. E. 1994. In Deterministic Chaos in General Relativity, Hobill, D., Burd, A., and Coley, A. (Eds.), Plenum, New York.
45. Rugh, S. E. (1990). Cand. Scient. Thesis, The Niels Bohr Institute.
46. Khalatnikov, L. M., Lifchitz, E. M., Khanin, K. M., Shchur, L. N., and Sinai, Ya. G. (1985). J. Stat. Phys. 38, 97.
47. Khalatnikov, L. M. (1999). Private communication, Erice, Sicily.
48. Khalatnikov, I. M., Lifshitz, E. M., Khanin, K. M., Shehur, L. N., and Sinai, Ya. G. (1985). J. Stat. Phys. 38, 1-2, 97-113.