Dynamical Systems / Chaos

  1. Collins C B: More Qualitative Cosmology, Commun. Math. Phys. 23 (1971), 137
    NB: Type-I/II/III/V/VI$_{h}$.
  2. Collins C B, J M Stewart: Qualitative Cosmology, Mon. Not. R. Astron. Soc. 153 (1971), 419
  3. Collins C B, S W Hawking: Why is the Universe Isotropic?, Astrophys. J. 180 (1973), 317
    NB: Focuses on Type-VII$_{h}$ and Type-VII$_{0}$ as they respectively contain the $k = -\,1$ and $k = 0$ FLRW cases. "Since it would seem that the existence of galaxies is a necessary condition for the development of intelligent life, the answer to the question `why is the Universe isotropic?' is `because we are there!'". Minimizes the chances that Misner's model might be realistic.
  4. Wainwright J, L Hsu: A Dynamical Systems Approach to Bianchi Cosmologies: Orthogonal Models of Class A, Class. Quantum Grav. 6 (1989), 1409
  5. Kawabe T, S Ohta: Onset of Chaos in Time-Dependent Spherically Symmetric SU(2) Yang-Mills Theory, Phys. Rev. D 41 (1990), 1983
    NB: Minkowskian background
  6. Woszczyna A, M Heller: Is a Horizon-Free Cosmology Possible?, Gen. Rel. Grav. 22 (1990), 1367
  7. Berger B K: Comment on the Computation of Liapunov Exponents for the Mixmaster Universe, Gen. Rel. Grav. 23 (1991), 1385
  8. Hewitt C G: Algebraic Invariant Curves in Cosmological Dynamical Systems and Exact Solutions, Gen. Rel. Grav. 23 (1991), 1363
  9. Szydlowski M, M Biesiada: Chaos in Mixmaster Models, Phys. Rev. D 44 (1991), 2369
  10. Coley A A, J Wainwright: Qualitative Analysis of Two-Fluid Bianchi Cosmologies, Class. Quantum Grav. 9 (1992), 651
    NB: non-interacting fluids, LRS $G_{3}$II, 3-D phase portraits, different $\gamma$'s.
  11. Hewitt C G, J Wainwright: Dynamical Systems Approach to Tilted Bianchi Cosmologies: Irrotational Models of Type V, Phys. Rev. D 46 (1992), 4242
    NB: LRS $G_{3}$
  12. Karas V, D Vokrouhlický: Chaotic Motion of Test Particles in the Ernst Space-Time, Gen. Rel. Grav. 24 (1992), 729
  13. Rangarajan R, M Srednicki: Chaotic Dark Matter, Phys. Rev. D 46 (1992), 3350
  14. Thirring W: Classical Dynamical Systems and Classical Field Theory (A Course in Mathematical Physics 1 and 2), (New York: Springer, 1992, 2nd ed)
  15. Woszczyna A: Gauge-Invariant Cosmic Structures - A Dynamic Systems Approach, Phys. Rev. D 45 (1992), 1982
  16. Berger B K: Note on Time Reversible Chaos in Mixmaster Dynamics, Phys. Rev. D 47 (1993), 3222
  17. Burd A, R Tavakol: Invariant Lyapunov Exponents and Chaos in Cosmology, Phys. Rev. D 47 (1993), 5336
  18. Calzetta E, C El Hasi: Chaotic Friedmann-Robertson-Walker Cosmology, Class. Quantum Grav. 10 (1993), 1825
    NB: $k=1$, conformally coupled real, free, massive scalar field.
  19. Hewitt C G, J Wainwright: A Dynamical Systems Approach to Bianchi Cosmologies: Orthogonal Models of Class B, Class. Quantum Grav. 10 (1993), 99
  20. Blanco S, G Domenech, C El Hasi, O A Rosso: Chaos in Classical Cosmology, Gen. Rel. Grav. 26 (1994), 1131
    NB: Conformally coupled massive scalar field in FLRW, use of techniques from Dynamical Systems Theory, fixed point analysis.
  21. Biesiada M: Searching for Invariant Description of Chaos in General Relativity, Class. Quantum Grav. 12 (1995), 715
    NB: Type-IX.
  22. Blanco S, A Costa, O A Rosso: Chaos in Classical Cosmology (II), Gen. Rel. Grav. 27 (1995), 1295
    NB: FLRW with conformally coupled, massive, self-interacting ($\Phi^{4}$) scalar field source and cosmological constant.
  23. LeBlanc V G, D Kerr, J Wainwright: Asymptotic States of Magnetic Bianchi VI$_{0}$ Cosmologies, Class. Quantum Grav. 12 (1995), 513
    NB: OSH Type-VI$_{0}$, $\gamma$-law perfect fluid flus sourcefree magnetic Maxwell field matter source.
  24. Vieira W M, P S Letelier: Curvature and Chaos in General Relativity, Class. Quantum Grav. 13 (1996), 3115
  25. Chicone C, B Mashoon, D G Retzloff: Gravitational Ionization: A Chaotic Net in the Kepler System, Class. Quantum Grav. 14 (1997), 699
  26. Cornish N J, J J Levin: The Mixmaster Universe is Chaotic, Phys. Rev. Lett. 78 (1997), 998. Also: Preprint gr-qc/9605029.
  27. LeBlanc V G: Asymptotic States of Magnetic Bianchi I Cosmologies, Class. Quantum Grav. 14 (1997), 2281
  28. Tavakol R: Introduction to Dynamical Systems, in Dynamical Systems in Cosmology, Eds. J Wainwright, G F R Ellis, (Cambridge: Cambridge University Press, 1997)
  29. Wainwright J, G F R Ellis (Eds.): Dynamical Systems in Cosmology, (Cambridge: Cambridge University Press, 1997)
  30. LeBlanc V G: Bianchi II Magnetic Cosmologies, Class. Quantum Grav. 15 (1998), 1607
  31. Wainwright J, M J Hancock, C Uggla: Asymptotic Self-Similarity Breaking at Late Times in Cosmology, Class. Quantum Grav. 16 (1999), 2577. Also: Preprint gr-qc/9812010.

Selected References
Last revision: Tue, 22-8-2000 (This page is under construction)