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Qualitative Cosmology

  • I. M. Khalatnikov
Chapter
Part of the Ettore Majorana International Science Series book series (EMISS, volume 56)

Abstract

The article surveys qualitative methods of the study of the simplest cosmological models of the Universe in the dissipation-free regime and in the presence of viscosity. For homogeneous cosmological models the Einstein equations reduce to a system ofregular differential equations with rspect to time. Further these equations are rewritten in the form of equations for a dynamical system permitting to analyze possible types of the evolution of solutions in the phase space of this system.

Keywords

Phase Plane Qualitative Theory Cosmological Evolution Gravity Equation Cosmological Singularity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    I. S. Shikin, The homogeneous axis-symmetric model in the ultra-relativistic case, Doklady Akademii Nauk 176: 1048–1051 (1967).Google Scholar
  2. 2.
    C. B. Collins, More qualitative cosmology, Comm. Math. Phys. 23: 137–144 (1971).ADSzbMATHGoogle Scholar
  3. 3.
    V. A. Belinsky, E.M.Lifshitz, I.M.Khalatnikov, Oscillatory regime of the approach to the singular point in relativistic cosmology, Uspekhi Fiz. Nauk 102: 463–500 (1970).CrossRefGoogle Scholar
  4. 4.
    V. A. Belinsky, E. M. Lifshitz, I. M. Khalatnikov, On the construction of the general cosmological solution of the Einstein equation with the singularity in time, ZhETF 62: 1606–1613 (1972).Google Scholar
  5. 5.
    O. I. Bogoyavlensky, S. P. Novikov, Peculiarities of the cosmological Biancchi-IX model in terms of the qualitative theory of differential equations, ZhETF 64: 1475–1494 (1973).Google Scholar
  6. 6.
    O. I. Bogoyavlensky, “Methods of the qualitative theory of dynamical systems in astrophysics and gas dynamics”, Nauka, Moscow (1980).Google Scholar
  7. 7.
    V. A. Belinsky, I.M.Khalatnikov, On the influence of viscosity on the character of cosmological evolution, ZhETF 69: 401–413Google Scholar
  8. 8.
    V. A. Belinsky, I. M. Khalatnikov, Viscosity effects in isotropic cosmology, ZhETF 72: 3–17 (1977).Google Scholar
  9. 9.
    E. S. Nikomarov, I. M. Khalatnikov, Qualitative isotropic cosmology with the cosmological constant with the dissipation taken into account, ZhETF 75: 1176–1180 (1978).Google Scholar
  10. 10.
    V. A. Belinsky, E. S. Nikomarov, I. M. Khalatnikov, The study of cosmological evolution of the viscous-elastic matter with causal thermodynamics ZhETF N 2: 417–433 (1979).Google Scholar
  11. 11.
    A. A. Andronov, E. A. Leontovich, I. I. Gordon, A. G. Mayer, The theory of bifurcations of dynamical systems on the plane“, Nauka, Moscow (1967).Google Scholar
  12. 12.
    A. A. Andronov, E. A. Leontovich, I. I. Gordon, A. G. Mayer, “Qualitative theory of the second-order dynamical systems”, Nauka, Moscow (1966).Google Scholar
  13. 13.
    V. A. Belinsky, I. M. Khalatnikov, On the influence of scalar and vector fields on the character of the cosmological singularity, ZhETF 63: 1121–1134 (1972).Google Scholar
  14. 14.
    V. A. Belinsky, I. M. Khalatnikov, On the influence of matter and physical fields upon the nature of cosmological singularities, in: “Soviet Physics Reviews”, Harwood Ac. Publ., Switzerland (1981).Google Scholar
  15. 15.
    L. D. Landau, E. M. Lifshitz, “Mechanics of continuous media”, Fizmatgiz, Moscow (1953).Google Scholar
  16. 16.
    G. L. Murphy, Big Bang model without singularities, Phys. Rev. D, 8: 4231–4233 (1973).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • I. M. Khalatnikov
    • 1
  1. 1.L.D.Landau Institute for Theoretical PhysicsUSSR Academy of SciencesUSSR

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