Billiard Representation for Multidimensional Quantum Cosmology near the   Singularity
  The degenerate Lagrangian system describing a lot of cosmological models is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the "singularity" is reduced to a billiard on the Lobachevsky space. The Wheeler-DeWitt equation in the asymptotical regime is solved and a third-quantized model is suggested. 
V. D. Ivashchuk and V. N. Melnikov