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Application: Cosmological Models of Bianchi Type, the Tumbling Universe

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2117)

Abstract

Cosmological models are solutions of the Einstein equations relating the geometry of spacetime—the curvature of a four-dimensional Lorentzian metric g—to the matter content. Bianchi models, in particular, are homogeneous but anisotropic solutions. They are given by a five-dimensional ODE system in expansion-reduced variables and feature the Kasner circle \(\mathcal{K}\) of equilibria and caps filled with heteroclinic orbits connecting equilibria on \(\mathcal{K}\). On the Kasner circle, we find three bifurcation points without parameters.

Keywords

  • Cosmological Model
  • Einstein Equation
  • Bifurcation Point
  • Heteroclinic Orbit
  • Bianchi Model

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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Fig. 13.1
Fig. 13.2

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Liebscher, S. (2015). Application: Cosmological Models of Bianchi Type, the Tumbling Universe. In: Bifurcation without Parameters. Lecture Notes in Mathematics, vol 2117. Springer, Cham. https://doi.org/10.1007/978-3-319-10777-6_13

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