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A class of exact solutions to the Belinski-Khalatnikov-Lifshitz (BKL)scenario is derived and tested for their stability against small perturbations.These are the only regular solutions in the Painlev\'{e} sense. We prove thatthey are unstable in the vicinity of the cosmological singularity. Regularityof the dynamics is also examined with the dynamical systems method. Our resultsconfirm the conjecture of BKL that the dynamics near the singularity becomesgenerically chaotic.

Generic instability of the dynamics underlying the Belinski-Khalatnikov-Lifshitz scenario