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Structurally stable approximations to Friedmann—Lemaître world models

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“Briser les contraintes de l'espace-temps, tel est le but ultime de l'homme: exploiter tous les modes d'action non locale qui peuvent être aisément contrôlés, c'est ce qu'exige l'humanité...” René Thom,Penser les mathématiques

Abstract

Friedmann—Lemaître cosmology is briefly reviewed in terms of dynamical systems. It is demonstrated that in certain cases bulk viscosity dissipation structurally stabilizes Friedmann—Lemaître solutions. It turns out that, for A=0, there are structurally stable solutions if ξ~ε1/2, where ξ is the bulk viscosity coefficient. For A≠0 structurally stable solutions are essentially those with ξ=const. The role of structural stability in physics and cosmology is shortly discussed.

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References

  • Arnold, V.: 1980,Chapitres supplementaires de la théorie des equations différentielles ordinaires ed. de Moscou.

  • Belinsky, V. A. and Khalatnikov, I. M.: 1975,Zh. Eksper. Teoret. Fiz. 69, 401.

    Google Scholar 

  • Bogoyavlenskij, O. I.: 1980,Metody Kachestvennoj Teorii Dinamicheskikh System w Astrofizikie i Gazovoj Dinamikie, Nauka, Moscow.

    Google Scholar 

  • Collins, C. B.: 1974,Comm. Math. Phys. 39, 131.

    Google Scholar 

  • Collins, C. B.: 1977,GRG 8, 717.

    Google Scholar 

  • Heller, M., Klimek, Z., and Suszycki, L.: 1973,Astrophys. Space Sci. 20 205.

    Google Scholar 

  • Heller, M. and Szydlowski, M.: 1983,Astrophys. Space Sci. 90 327 (this issue).

    Google Scholar 

  • Klimek, Z.: 1981,Acta Cosm. 10, 7.

    Google Scholar 

  • Murphy, G. L.: 1973,Phys. Rev. D8, 4231.

    Google Scholar 

  • Peixoto, M.: 1962,Topology 1, 747.

    Google Scholar 

  • Prigogine, I. and Stengers, I.: 1979,La nouvelle alliance, Gallimard.

  • Robertson, H. P.: 1933,Rev. Mod. Phys. 5, 62.

    Google Scholar 

  • Smale, S.: 1980,The Mathematics of Time, Springer, Berlin.

    Google Scholar 

  • Stabell, R. and Refsdal, S.: 1966,Monthly Notices Roy. Astron. Soc. 132, 379.

    Google Scholar 

  • Suszycki, L.: 1978,Acta Cosm. 7, 147.

    Google Scholar 

  • Szydlowski, M. and Heller, M.: 1982,Acta Phys. Pol. B13. 375.

    Google Scholar 

  • Thom, R.: 1977,Stabilité structurelle et morphogén⪻se (deuxième éd.), Interéditions.

  • Tolman, R. C.: 1934,Relativity, Thermodynamics and Cosmology, Clarendon Press, Oxford.

    Google Scholar 

  • Woszczyna, A.: 1980,Acta Phys. Pol. B 11, 15.

    Google Scholar 

  • Woszczyna, A. and Betkowski, W.: 1982,Astrophys. Space Sci. 82, 489.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Astronomical Observatory of the Jagiellonian University, Cracow, Poland

    Z. Golda

  2. Department of Philosophy, Pontifical Academy of Theology, Cracow, Poland

    M. Heller

  3. Specola Vaticana, Castel Gandolfo, Vatican City State

    M. Heller

  4. Department of Philosophy, Pontifical Academy of Theology, Cracow, Poland

    M. Szydlowski

Authors
  1. Z. Golda
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  2. M. Heller
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  3. M. Szydlowski
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Golda, Z., Heller, M. & Szydlowski, M. Structurally stable approximations to Friedmann—Lemaître world models. Astrophys Space Sci 90, 313–326 (1983). https://doi.org/10.1007/BF00650065

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