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2 The BKL Phenomenon

In this section, we explain the main ideas of the billiard description of the BKL behavior. Our approach is based on the billiard review [48Jump To The Next Citation Point], from which we adopt notations and conventions. We shall here only outline the logic and provide the final results. No attempt will be made to reproduce the (sometimes heuristic) arguments underlying the derivation.

 2.1 The general action
 2.2 Hamiltonian description
  2.2.1 Action in canonical form
  2.2.2 Iwasawa change of variables
 2.3 Decoupling of spatial points close to a spacelike singularity
  2.3.1 Spatially homogeneous models
  2.3.2 The ultralocal Hamiltonian
  Comments
 2.4 Dynamics as a billiard in hyperbolic space
  Comments
 2.5 Rules for deriving the wall forms from the Lagrangian – Summary
 2.6 More on the free motion: The Kasner solution
 2.7 Chaos and billiard volume
 2.8 A note on the constraints
 2.9 On the validity of the BKL conjecture – A status report

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