Honoring the 90th birthday of Academician IMKhalatnikov (Scientific session of the Physical Sciences Division of the Russian Academy of Sciences, 21 October 2009)

摘要

We consider different aspects of the problem of cosmological singularities, such as the Belinsky±Khalatnikov±Lifshitz (BKL) oscillatory approach to a singularity, the new features of cosmological dynamics in the neighborhood of a singular- ity in multidimensional and superstring cosmological models, and their connections with modern branches of mathematics such as infinite-dimensional Lie algebras. The chaoticity of the oscillatory approach to the cosmological singularity is also discussed. The conclusions contain some thoughts about the past and the future of the Universe in light of theoscillatory approach to the Big Bang and the Big Crunch cosmological singularities.