• DOI:10.1134/S0202289309010137
• Corpus ID: 17301606

On the billiard approach in multidimensional cosmological models

@article{Ivashchuk2008OnTB,
  title={On the billiard approach in multidimensional cosmological models},
  author={Vladimir D. Ivashchuk and Vitaly N. Melnikov},
  journal={Gravitation and Cosmology},
  year={2008},
  volume={15},
  pages={49-58}
}

• V. Ivashchuk, V. Melnikov
• Published 17 November 2008
• Mathematics
• Gravitation and Cosmology

A short overview of the billiard approach for cosmological-type models with n Einstein factor spaces is presented. We start with the billiard representation for pseudo-Euclidean Toda-like systems of cosmological origin. Then we consider cosmological models with a multicomponent perfect-fluid and with composite branes. The second case describes cosmological and spherically symmetric configurations in a theory with scalar fields and fields of forms. The conditions for appearance of asymptotic Kasnerlike and oscillating behaviors in the limits τ → +0 and τ → +∞ (where τ is the synchronous variable) are formulated (e.g., in terms of inequalities for Kasner parameters). Examples of billiards related to the hyperbolic Kac-Moody algebras E10, AE3 and A1,II are given.