Advertisement

General Relativity and Gravitation

, Volume 19, Issue 7, pp 707–718 | Cite as

Generic and nongeneric world models

  • Zdzislaw A. Golda
  • Marek Szydlowski
  • Michal Heller
Research Articles

Abstract

Catastrophe theory methods are employed to obtain a new classification of those world models which can be presented in the form of gradient dynamical systems. Generic sets and structural stability of models in the potential space are strictly defined. It is shown that if a cosmological model is required to be Friedman and generic, it must be flat.

Keywords

Dynamical System Structural Stability Differential Geometry Cosmological Model Theory Method 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Misner, C. W. (1968).Astrophys. J.,151, 431.Google Scholar
  2. 2.
    Ellis, G. F. R. (1983). Proceedings of the GR-10 Conference, Bertotti, B., de Felice, F., Pascolini, A., eds., Consiglio Nazionale delle Ricerche. (Roma, Preprint).Google Scholar
  3. 3.
    Marsden, J. E. (1981). Lectures on Geometric Methods in Mathematical Physics. (Society of Industrial Applied Mathematics, Philadelphia).Google Scholar
  4. 4.
    Fischer, A. E., Marsden, J. E., and Moncrief, V. (1980). InEssays in General Relativity. A Festschrift for Abraham Taub, F. J. Tipler, ed. (Academic Press, New York).Google Scholar
  5. 5.
    Brill, D. (1982). InSpace-Time and Geometry, The Alfred Schild Lectures, R. A. Matzner and L. C. Shepley, eds. (University of Texas Press, Austin).Google Scholar
  6. 6.
    Brocker, Th. and Lander, L. (1975).Differentiable Germs and Catastrophes. (Cambridge University Press, Cambridge).Google Scholar
  7. 7.
    Milnor, J. (1963).Morse Theory. (Princeton University Press, Princeton, New Jersey).Google Scholar
  8. 8.
    Smale, S. (1980).The Mathematics of Time. (Springer-Verlag, New York).Google Scholar
  9. 9.
    Arnold, W. I. (1983).The Theory of Catastrophes (Moscow University Press, Moscow).Google Scholar
  10. 10.
    Bogoyavlensky, O. I. (1980).Methods of a Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics. (Nauka, Moscow, in Russian).Google Scholar
  11. 11.
    Belinsky, V. A. and Khalatnikov, I. M. (1975).Zh. Eksp. Tear. Fiz.,69, 401. [Sov. Phys. JETP,42, 205.]Google Scholar
  12. 12.
    Ellis, G. F. R. (1973). InCargese Lectures, Vol. 5, E. Schatzmann, ed. (Gordon and Breach, New York).Google Scholar
  13. 13.
    Novello, M. and Reboucas, M. J. (1978).Astrophys. J.,225, 719.Google Scholar
  14. 14.
    Stabell, R. and Refsdal, S. (1966).Month. Not. Roy. Astron. Soc.,132, 379.Google Scholar
  15. 15.
    Pommaret, J. F. (1978).Systems of Partial Differential Equations and Lie Pseudogroups. (Gordon and Breach, New York).Google Scholar
  16. 16.
    Wassermann, G. (1974).Stability of Unfoldings. (Springer-Verlag, Berlin).Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • Zdzislaw A. Golda
    • 1
  • Marek Szydlowski
    • 2
  • Michal Heller
    • 3
  1. 1.N. Copernicus Astronomical CenterPolish Academy of SciencesCracowPoland
  2. 2.Astronomical ObservatoryJagellonian UniversityCracowPoland
  3. 3.Faculty of PhilosophyVatican Astronomical Observatory, Vatican City State, and Pontifical Academy of CracowCracowPoland

Personalised recommendations