Dynamics of the General Bianchi IX Model near a Cosmological Singularity

Half a century ago, Belinsky and Khalatnikov proposed generic solution of the Einstein equations near their cosmological singularity, based on generalization homogeneous model Bianchi type IX. Consideration evolution most general non-diagonal case this is greatly simplified if it assumed that, when approaching singularity t=0, reduces to so-called asymptotic dynamics, at which inequality (6) holds. It has been suggested that continues be true from moment its first fulfilment up space-time. We analyze assumption show incorrect in case. However, shown there always time t_0, after becomes true. The value t_0 smaller less degree non-diagonality model. Some details behaviour IX are considered stage dynamics singularity.