The Belinskii-Khalatnikov-Lifshitz Discrete Evolution as an Approximation to Mixmaster Dynamics

  • Beverly K. Berger
Part of the NATO ASI Series book series (NSSB, volume 332)


Mixmaster dynamics is defined to be the evolution of vacuum, diagonal Bianchi IX spatially homogeneous cosmologies. Belinskii, Lifshitz, and Khalatnikov (BKL) developed a discrete approximation to Mixmaster dynamics. Here we analyze their approximation to discuss how well it represents the true solution. We show that sufficiently close to the singularity, the BKL approximation describes all the features of an accurately computed Mixmaster trajectory. Within the BKL approximation, the origination of any sensitivity to initial conditions can be explicitly identified. Since a precise analogy can be drawn between the BKL parameters and variables which describe the true Mixmaster dynamics, it can be argued that the trajectories inherit any chaos that characterizes the approximation. Since the discrete evolution which is the closest analog of the true dynamics is only “marginally chaotic,” recent controversies over whether or not the dynamics is chaotic may be more semantic than substantive.


Bianchi Type Hamiltonian Constraint Potential Wall Expansion Direction Liapunov Exponent 
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 Science+Business Media New York 1994

Authors and Affiliations

  • Beverly K. Berger
    • 1
  1. 1.Physics DepartmentOakland UniversityRochesterUSA

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