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Structural stability properties of friedman cosmology

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Abstract

A dynamical system with Robertson-Walker symmetries and the equation of the statep=γ∈, 0≤γ≤1, considered both as a conservative and nonconservative system, is studied with respect to its structural stability properties. Different cases are shown and analyzed on the phase space (x=R D, y=x).

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References

  1. Andronov, A. A., and Pontryagin, L. S. (1937).Dokl. Akad. Nauk SSSR,14, 247.

    Google Scholar 

  2. Arnold, V. (1980). Chapitres supplementaires de la théorie des equations différentielles ordinaries. (Ed. de Moscou).

  3. Poston, T., and Steward, I. (1978).Catastrophy Theory and Its Applications (Pitman, London).

    Google Scholar 

  4. Eddington, A. S. (1930).M. Not. R. Astron. Soc.,90, 668.

    Google Scholar 

  5. Collins, C. B. (1974).Commun. Math. Phys.,39, 131.

    Google Scholar 

  6. Golda, Z., Heller, M., and Szydlowski, M. (1983).Astrophys. Space Sci.,90, 313.

    Google Scholar 

  7. Peixoto, M. (1962).Topology,1, 101.

    Google Scholar 

  8. Smale, S. (1980).The Mathematics of Time (Springer, New York).

    Google Scholar 

  9. Abraham, R., and Marsden, J. (1967).Foundations of Mechanics (Benjamin, New York).

    Google Scholar 

  10. Bogoyavlenskij, O. I. (1980).Methods of a Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics (Nauka, Moscow), (in Russian).

    Google Scholar 

  11. Weinberg, S. (1911).Astrophys. J.,168, 175.

    Google Scholar 

  12. Klimek, Z. (1971).Post. Astr.,19, 165 (in Polish).

    Google Scholar 

  13. Heller, M., Klimek, Z., and Suszycki, L. (1973).Astrophys. Space Sci.,20, 205.

    Google Scholar 

  14. Murphy, G. (1973).Phys. Rev. D,8, 4231.

    Google Scholar 

  15. Belinsky, V. A., and Khalatnikov, I. M. (1975).Zh. Eksp. Teor. Fiz.,60, 401, [Sov. Phys. JETP,42, 205].

    Google Scholar 

  16. Belinsky, V. A., and Khalatnikov, I. M. (1977).Zh. Eksp. Teor. Fiz.,72, 3, [Sov. Phys. JETP,45, 1].

    Google Scholar 

  17. Nikomarov, E. S., and Khalatnikov, I. M. (1978).Zh. Eksp. Teor. Fiz.,75, 1176, [Sov. Phys. JETP,48, 592, (1978)].

    Google Scholar 

  18. Suszycki, L. (1978).Acta Cosm.,7, 147.

    Google Scholar 

  19. Klimek, Z. (1981).Acta Cosm.,10, 7.

    Google Scholar 

  20. Heller, M., and Klimek, Z. (1974).Astrophys. Space Sci.,33, L37.

    Google Scholar 

  21. Heller, M. (1978).Acta Cosmol.,7, 7.

    Google Scholar 

  22. Woszczyna, A. (1980).Acta Phys. Pol.,B11, 15.

    Google Scholar 

  23. Woszczyna, A. and Betkowski, W. (1981).Astrophys. Space Sci.,82, 489.

    Google Scholar 

  24. Heller, M., Ostrowski, M., Woszczyna, A., and Szydlowski, M. (1982).Astrophys. Space Sci.,87, 425 (the name of the last of the authors has been mistakenly omitted in print).

    Google Scholar 

  25. Szydlowski, M., and Heller, M. (1982).Acta Phys. Pol.,B13, 375.

    Google Scholar 

  26. Szydlowski, M., and Heller, M. (1983).Acta Phys. Pol.,B14, 303.

    Google Scholar 

  27. Heller, M., and Szydlowski, M. (1983).Astrophys. Space Sci.,90, 327.

    Google Scholar 

  28. Tolman, R. C. (1934).Relativity, Thermodynamics and Cosmology (Clarendon Press, Oxford).

    Google Scholar 

  29. Nemytskij, V. V., and Stepanov, V. V. (1960).Qualitative Theory of Differential Equations (Princeton University Press, Princeton).

    Google Scholar 

  30. Sansone, G., and Conti, R. (1964).Non-Linear Differential Equations (Pergamon Press, Oxford).

    Google Scholar 

  31. Robertson, H. P., and Noonan, T. W. (1968).Relativity and Cosmology (Saunders, Philadelphia).

    Google Scholar 

  32. Robertson, H. P. (1933).Rev. Mod. Phys.,5, 62.

    Google Scholar 

  33. Andronov, A. A., Vitt, A. A., and Khajkin, S. Eh. (1981).Theory of Oscillations (Nauka, Moscow), (in Russian).

    Google Scholar 

  34. Kolb, E. W., and Wolfram, S. (1980).Astrophys. J.,239, 428.

    Google Scholar 

  35. Thorn, R. (1977). Stabilité structurelle et morphogénèse, (deuxième edition, Inter-Editions, Paris).

    Google Scholar 

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Szydlowski, M., Heller, M. & Golda, Z. Structural stability properties of friedman cosmology. Gen Relat Gravit 16, 877–890 (1984). https://doi.org/10.1007/BF00762940

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