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Ergodic theory of the mixmaster universe in higher space-time dimensions. II

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Abstract

The topological dynamics of the mixmaster models in space-time dimension d+1 are investigated. We use a new parametrization to reduce the mixmaster map to a translation combined with an appropriate isometry or a dilating inversion. For d⩽9, we show that the mixmaster map is ergodic and topologically mixing. For d⩾10, the mixmaster map reduces to the identity after a finite number of iterations, except for a set of initial data with zero Lebesgue measure.

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References

  1. V. M. Alekseev and M. V. Yakobson,Phys. Rep. 75:287–325 (1981).

    Google Scholar 

  2. J. D. Barrow,Phys. Rep. 85:1–49 (1982).

    Google Scholar 

  3. J. D. Barrow, inClassical General Relativity, W. B. Bonner, J. N. Islam, and M. A. H. MacCallum, eds. (Cambridge University Press, Cambridge, 1984), pp. 26–41.

    Google Scholar 

  4. J. D. Barrow and F. J. Tipler,Phys. Rep. 56:371–02 (1979).

    Google Scholar 

  5. J. D. Barrow and J. Stein-Schabes,Phys. Rev. D 32:1595–1596 (1985).

    Google Scholar 

  6. V. A. Belinskii, I. M. Khalatnikov, and E. M. Lifshitz,Adv. Phys. 19:525–573 (1970).

    Google Scholar 

  7. V. A. Belinskii, I. M. Khalatnikov, and E. M. Lifshitz,Phys. Lett. 77A:214–216 (1980).

    Google Scholar 

  8. D. F. Chernoff and J. D. Barrow,Phys. Rev. Lett. 50:134–137 (1983).

    Google Scholar 

  9. I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai,Ergodic Theory (Springer, Berlin, 1982).

    Google Scholar 

  10. J. Demaret, M. Henneaux, and P. Spindel,Phys. Lett. 164B:27–30 (1985).

    Google Scholar 

  11. J. Demaret, J. L. Hanquin, M. Henneaux, P. Spindel, and A. Taormina,Phys. Lett. 175B:129–132 (1986).

    Google Scholar 

  12. Y. Elskens and M. Henneaux, Ergodic theory of the mixmaster model in higher space-time dimensions,Nucl. Phys. B, in press.

  13. Y. Elskens and M. Henneaux, Chaos in Kaluza-Klein models,Class. Quant. Gravity, in press.

  14. T. Furusawa and A. Hosaya,Prog. Theor. Phys. 73:467–175 (1985).

    Google Scholar 

  15. P. Halpern,Phys. Rev. D 33:354–362 (1986).

    Google Scholar 

  16. H. Ishihara,Prog. Theor. Phys. 74:490–500 (1985).

    Google Scholar 

  17. I. M. Khalatnikov, E. M. Lifshitz, K. M. Khanin, L. M. Shchur, and Ya. G. Sinaï,J. Stat. Phys. 38:97–114 (1985).

    Google Scholar 

  18. E. M. Lifshitz, I. M. Lifshitz, and I. M. Khalatnikov,Sov. Phys. JETP 32:173–180 (1971).

    Google Scholar 

  19. C. W. Misner,Phys. Rev. Lett. 22:1071–1074 (1969).

    Google Scholar 

  20. M. P. Ryan and L. C. Shepley,Homogeneous Relativislic Cosmologies (Princeton University Press, Princeton, 1974).

    Google Scholar 

  21. A. Tomimatsu and H. Ishihara,Gen. Rel. Grav. 18:161–171 (1986).

    Google Scholar 

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Authors and Affiliations

  1. Faculté des Sciences, Université Libre de Bruxelles, CP 231, B-1050, Bruxelles, Belgium

    Yves Eiskens

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  1. Yves Eiskens
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Chargé de recherches au Fonds National de la Recherche Scientifique.

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Eiskens, Y. Ergodic theory of the mixmaster universe in higher space-time dimensions. II. J Stat Phys 48, 1269–1282 (1987). https://doi.org/10.1007/BF01009545

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