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Communications in Mathematical Physics

, Volume 305, Issue 1, pp 59–83 | Cite as

Ancient Dynamics in Bianchi Models: Approach to Periodic Cycles

  • S. LiebscherEmail author
  • J. Härterich
  • K. Webster
  • M. Georgi
Article

Abstract

We consider cosmological models of Bianchi type. In particular, we are interested in the α-limit dynamics near the Kasner circle of equilibria for Bianchi classes VIII and IX. They correspond to cosmological models close to the big-bang singularity.

We prove the existence of a codimension-one family of solutions that limit, for t → −∞, onto a heteroclinic 3-cycle to the Kasner circle of equilibria. The theory extends to arbitrary heteroclinic chains that are uniformly bounded away from the three critical Taub points on the Kasner circle, in particular to all closed heteroclinic cycles of the Kasner map.

Keywords

Homoclinic Orbit Stable Manifold Periodic Cycle Graph Transformation Heteroclinic Orbit 
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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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • S. Liebscher
    • 1
    Email author
  • J. Härterich
    • 2
  • K. Webster
    • 3
  • M. Georgi
    • 1
  1. 1.Institut für MathematikFreie Universität BerlinBerlinGermany
  2. 2.Fakultät für Mathematik Ruhr-UniversitätUniversitätsstr. 150BochumGermany
  3. 3.Department of MathematicsImperial College LondonLondonUK

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